President-elect Donald J. Trump leaving his clubhouse for dinner at the Trump National Golf Club Bedminster in New Jersey on Saturday night.

BEDMINSTER, N.J. — President-elect Donald J. Trump hinted strongly on Sunday that he was considering picking James N. Mattis, a retired Marine Corps general, to be defense secretary, heaping praise on the general for the second day in a row as he sought to complete his choices for a national security team.

The president-elect, who met with the general on Saturday at Trump National Golf Club here in Bedminster, wrote on Twitter: “General James ‘Mad Dog’ Mattis, who is being considered for Secretary of Defense, was very impressive yesterday. A true General’s General!”

That followed similar remarks to reporters on Saturday after the meeting at the golf club, where Mr. Trump is sitting down with advisers and interviewing what he called “numerous patriots” throughout the weekend. In brief comments on Saturday, Mr. Trump called General Mattis “just a brilliant, wonderful man.”

“What a career — we are going to see what happens, but he is the real deal,” the president-elect added.

In addition to his praise of General Mattis, Mr. Trump used other Twitter posts early Sunday to lash out at his critics on Broadway and in late-night television. But in remarks to reporters and in appearances on Sunday morning news programs, Mr. Trump’s advisers sought to focus on the efforts to staff the new administration.

“We’re going to have a great day,” Mr. Trump told reporters outside his golf resort. “Great people coming. You’ll see. Great people. Thank you.” Asked whether he planned to make any appointments on Sunday, the president-elect said: “I think so. I think so. It could very well happen.”

Some of those appointments could represent a shift away from the hard-line national security picks he announced last week, including Senator Jeff Sessions of Alabama to be attorney general and General Michael T. Flynn to be national security adviser.

On Sunday, Mr. Trump was set to meet with Rudolph W. Giuliani, a former mayor of New York. A loyal adviser to Mr. Trump during the campaign, Mr. Giuliani has been under consideration for secretary of state, though he is apparently in competition with several others, including David H. Petraeus, the retired four-star general who served as President Obama’s C.I.A. director before leaving amid revelations that he had provided classified information to a woman with whom he was having an affair.

Mr. Trump is also thinking of giving the secretary of state post to Mitt Romney, who called Mr. Trump a “phony” during the campaign.

The president-elect met on Saturday with Mr. Romney, the 2012 Republican presidential nominee and one of Mr. Trump’s fiercest critics during the 2016 campaign. Aides to both men say that despite the exceedingly harsh words between the two during the Republican primary, Mr. Romney is under consideration to lead the State Department.

“I can say that Governor Romney is under active and serious consideration to serve as secretary of state of the United States,” Vice President-elect Mike Pence said on CBS’s “Face the Nation” program.

Mr. Trump is scheduled to remain in New York early next week, and aides declined to dispute a report in The New York Post that Melania Trump, the future first lady, and the couple’s son, Barron, would not be moving to the White House right away next year.

Jason Miller, a spokesman for the transition effort, said that “no formal statement has been released yet” regarding the Trump family’s transition to Washington. But he added, “One thing I will say is that there is obviously a sensitivity to pulling their 10-year-old out of school in the middle of the school year.”

Keeping Barron in New York could minimize the public scrutiny on him, a concern that first ladies have expressed in the past when arriving at the White House with young children.

If Ms. Trump does not immediately move to Washington, that could increase the likelihood that Mr. Trump will try to split his early months as president between the White House and Trump Tower in New York. The president-elect clearly enjoys his gold-plated office at Trump Tower and could break with tradition and conduct a significant amount of business there.

Mr. Trump’s consideration of General Mattis, who is widely respected throughout the military, could also signal an effort to ease concerns among members of the Washington establishment about the shape of his cabinet.

General Mattis, who led the First Marine Division during the 2003 invasion of Iraq to topple Saddam Hussein, later commanded American troops during the hard-fought battle to retake Falluja from Sunni insurgents in 2004. As head of the Central Command, General Mattis was heavily involved in plans to counter Iran’s military and protect the sea lanes in the Persian Gulf.

But his argument for a tougher military posture against Iran at times clashed with the views of President Obama and his national security team. General Mattis, who would be the first former ranking general to become defense secretary since George Marshall in the early 1950s, would need a congressional waiver to take office, since federal law stipulates that the Pentagon chief be out of uniform for seven years. General Mattis retired from the Marines in 2013.

General Mattis is not the only retired military commander Mr. Trump has considered for defense secretary. Last week, Mr. Pence sounded out Gen. Jack Keane, a former Army vice chief of staff, for the job. But General Keane said he had withdrawn his name from consideration, in part because he was still dealing with the death of his wife, Theresa, last June.

As Mr. Trump moves to complete his national security team, he may soon turn his attention to domestic affairs. Aides have said that members of the transition effort’s economic and domestic policy teams will fan out to meet with agency officials starting on Monday.

And Mr. Trump continued his practice of early-morning bursts on Twitter. Before attending church with Mr. Pence, Mr. Trump once again condemned the cast of “Hamilton” for its onstage appeal on Friday night to Mr. Pence — who was in the audience — to uphold the rights of a “diverse America.”

“The cast and producers of Hamilton, which I hear is highly overrated, should immediately apologize to Mike Pence for their terrible behavior,” Mr. Trump wrote.

Even as Mr. Trump bemoaned the actions of the cast of “Hamilton,” a smash hit on Broadway, Mr. Pence said on Sunday morning that he was not offended or bothered. In an appearance on “Fox News Sunday,” Mr. Pence said he would “leave it to others” to decide whether the theater was an appropriate place for a political message.

“‘Hamilton’ is just an incredible production and just incredibly talented people,” Mr. Pence said. “It was a real joy to be there.”

Mr. Pence said that when he heard boos from the audience, he told his daughter, who was also in attendance, “That’s what freedom sounds like.”

Mr. Trump, however, appears less willing to be magnanimous toward those in the entertainment business who criticize his nascent administration.

In another Twitter post, the president-elect expressed his disapproval of “Saturday Night Live,” calling it a “totally one-sided, biased show — nothing funny at all.” Mr. Trump was portrayed on the show as being overwhelmed by the prospect of being president.

Mr. Trump’s clash with his cultural critics came as he remained hunkered down at his golf resort to deliberate about his next appointments. He was scheduled to receive a series of high-profile visitors on Sunday, including Gov. Chris Christie of New Jersey and Kris W. Kobach, the secretary of state in Kansas.

It was in the low 40s on Sunday in Bedminster with gusty winds. Overnight, Mr. Trump had a series of tents with heaters erected in front of the clubhouse for members of the news media camped outside. “Not too cold out there I hope, right?” Mr. Trump said as he walked into the clubhouse. “If it is, come on in.”

As he entered the clubhouse, Ari Emanuel, the brother of Rahm Emanuel, President Obama’s former White House chief of staff and the current mayor of Chicago, arrived for a meeting. Ari Emanuel is a chief executive of William Morris Endeavor, a talent and media agency, and was the inspiration for a character on the HBO series “Entourage.”

“King of Hollywood,” Mr. Trump said while pointing at him. It was unclear whether Mr. Trump was considering Mr. Emanuel for a job in his administration.

But even as Mr. Trump’s transition team appeared eager to embrace a more disciplined approach to the process of building out his administration, the president-elect’s Twitter complaints about “Hamilton” and “Saturday Night Live” provided a distraction.

That may have been the intention. Mr. Trump’s Twitter posts diverted attention from other issues, including a $25 million settlement in a lawsuit against Trump University, concerns about conflicts of interest involving the president-elect’s business dealings, and questions about the propriety of potentially appointing his son-in-law, Jared Kushner, to a White House post.

Mr. Trump’s criticism of the “Hamilton” cast has captured widespread media coverage. In a statement read to the audience by the actor Brandon Victor Dixon, who plays Vice President Aaron Burr, the cast urged Mr. Pence and Mr. Trump to “uphold our American values” and “work on behalf of all of us.”

Mr. Trump reacted by calling the cast members “very rude and insulting” to Mr. Pence and claimed that they “couldn’t even memorize lines.” He later deleted the Twitter post about the cast’s supposed faulty memory.

Mr. Pence took a less combative stance. Addressing what he called “the center of the message” directed toward him, Mr. Pence said he understood that many Americans were disappointed and anxious about the election results.

“I just want to reassure people that what President-elect Donald Trump said on election night he absolutely meant from the bottom of his heart,” he said. “He is preparing to be the president of all of the people of the United States of America.”