Trump made the 90-minute drive back to Manhattan late Sunday after two days in Bedminster, and no new picks were revealed
The Republican billionaire-turned-world leader signaled he is seriously considering retired Marine Corps general James "Mad Dog" Mattis to be his Pentagon chief, heaping praise on him.
When asked before dinner at his Trump National Golf Club in New Jersey if he would soon reveal new nominations, Trump told reporters: "Pretty true," confirming he had "made a couple of deals."
But Trump made the 90-minute drive back to Manhattan late Sunday after two days in Bedminster, and no new picks were revealed.
Beyond Mattis, the top names on the guest list Sunday were Republican New Jersey Governor Chris Christie, who was recently ousted as the leader of Trump's transition team, former New York mayor Rudy Giuliani and immigration hardliner Kris Kobach.
The president-elect was clearly seeking to sound out people from a wide range of backgrounds, from party stalwarts to business moguls and former rivals.
Some of Trump's choices for other key posts so far -- attorney general, national security adviser and chief White House strategist -- have come under fire on civil rights grounds from Democrats and other critics.
But he has also moved to mend fences with moderate Republicans as he goes about building a new administration before his January 20 inauguration.
On Saturday, he interviewed one-time foe Mitt Romney -- the 2012 Republican presidential candidate who called him a "fraud" during the recent campaign -- for the secretary of state position reportedly coveted by Giuliani.
Trump, 70, was clearly wowed by Mattis, who led the US Central Command from 2010-2013, overseeing the US withdrawal from Iraq and a surge in Afghanistan.
"General James 'Mad Dog' Mattis, who is being considered for Secretary of Defense, was very impressive yesterday. A true General's General!" Trump said on Twitter.
Trump called the 66-year-old "the real deal" after their meeting Saturday.
A colorful combat commander and voracious reader, Mattis has been quoted as saying: "Be polite, be professional, but have a plan to kill everyone you meet."
Retired general Jack Keane told NPR that he had declined an offer to serve as Pentagon chief, citing personal reasons. He said he had recommended Mattis and retired general David Petraeus, a former CIA chief.
Christie, who threw his support to Trump after his own bid for the Republican presidential nomination fizzled, appeared back in favor after being pushed out as transition chief.
The campaign said the pair had a "productive discussion" Sunday on law enforcement and domestic security.
Others meeting Trump on Sunday included Wilbur Ross, under consideration for commerce secretary, global investor David McCormick, real estate investor Jonathan Gray and Bob Johnson, the founder of Black Entertainment Television (BET).
Trump's picks so far include ultra-conservative Senator Jeff Sessions as attorney general, hawkish congressman Mike Pompeo as CIA director and retired lieutenant general Michael Flynn as his national security adviser.
His choice of Steve Bannon, seen as an ideologue of the ultra-conservative alt-right movement, as chief strategist has also drawn fire.
Trump and Vice President-elect Mike Pence began their day attending a Sunday service at a Presbyterian church in the New Jersey countryside.
But the early-rising Trump was on Twitter before that, attacking the cast of hit Broadway musical "Hamilton" as rude, and "Saturday Night Live," the late-night satirical show that mercilessly lampoons him, as offering "nothing funny at all."
Pence was booed at a performance of "Hamilton" on Friday and one of the lead actors read out an appeal for the new administration to "work on behalf of all of us."
"The cast and producers of Hamilton, which I hear is highly overrated, should immediately apologize to Mike Pence for their terrible behavior," Trump wrote early Sunday, in his third tweet on the subject.
Pence told "Fox News Sunday" that he was not offended, and urged people to see the musical.
Trump spokesman Jason Miller told reporters that "there's obviously sensitivity to pulling their 10-year-old out of school in the middle of the school year," while not confirming the report.
Later in the day, Trump said his third wife and youngest son would join him in Washington "very soon, after he's finished with school."
And in Peru, US President Barack Obama offered his successor some unsolicited counsel.
"The main advice that I give to the incoming president is the United States really is an indispensable nation in our world order," Obama said as he wrapped up his final foreign trip.
The United States upholding "international norms and rules. That's what's made the modern world," Obama said.