"General James "Mad Dog" Mattis, who is being considered for Secretary of Defense, was very impressive yesterday. A true General's General!" Trump tweeted.
The two men met for a little over an hour Saturday afternoon in Bedminster, New Jersey. An official familiar with the transition process characterized it to CNN on Saturday as an important meeting.
Mattis can be considered a leading candidate for secretary of defense, the source said.
The source cautioned it's not a done deal but said Trump has been extremely impressed with Mattis' resume and what he's heard about him from others and at this stage is leaning in that direction.
Asked by reporters if he would choose Mattis to lead the Defense Department, Trump said, "All I can say is he is the real deal. He is the real deal."
On Monday, Senator John McCain, chairman of the Senate Armed Services Committee, threw his support behind Mattis.
"I am pleased that the President-elect found General Jim Mattis as impressive as I have in the many years I have had the privilege of knowing him," McCain said in a statement. General Mattis is one of the finest military officers of his generation and an extraordinary leader who inspires a rare and special admiration of his troops ... General Mattis has a clear understanding of the many challenges facing the Department of Defense, the U.S. military, and our national security. I hope he has an opportunity to serve America again."
In Mattis, Trump has a candidate who was held in high regard throughout the ranks of the Marine Corps during his 44 years of service. A seasoned combat commander, he led a task force into southern Afghanistan in 2001 and a Marine division at the time of the Iraq invasion in 2003.
The retired four-star general, who was known as "Mad Dog," was lauded for his leadership of Marines in the 2004 Battle of Falluja in Iraq -- one of the bloodiest of the war.
But he attracted controversy in 2005 when he said "it's fun to shoot some people
" while addressing service members in San Diego.
He also served as a commander of a major NATO strategic command, Allied Command Transformation, in Norfolk, Virginia.
Mattis, known as a plain-spoken leader well-liked by his Marines, was later promoted to run US Central Command in 2010 -- a post that gave him command responsibility for all US forces in the Middle East. He also was an outspoken critic of the Iran nuclear deal.
But should Trump decide to choose Mattis for the Pentagon, his 2013 retirement would create at least one hurdle: A retired officer is required to be out of uniform for at least seven years before taking control of the sprawling Pentagon responsibilities.
Mattis would require a waiver from Congress to be eligible for the position -- something that, with Republicans in control on Capitol Hill and the general praise for the general's career, would likely be a formality to obtain.
The President-elect on Friday announced three picks to lead his national security team: retired Army Lt. Gen. Michael Flynn as national security adviser, US Rep. Mike Pompeo of Kansas for CIA chief and Sen. Jeff Sessions of Alabama as attorney general.
Earlier Saturday, Trump met with 2012 GOP nominee Mitt Romney
, who was a harsh critic of the presidential candidate during the campaign. The two former rivals discussed foreign affairs amid speculation that Romney could be a candidate for secretary of state.
Trump on Sunday met with a swath of visitors. Among those visiting the President-elect were former New York City Mayor Rudy Giuliani, New Jersey Gov. Chris Christie, Kansas Secretary of State Kris Kobach and BET founder Robert Johnson.
"It went very well," Trump said after the meeting with Christie, a GOP primary rival turned supporter, who previously helmed the President-elect's transition efforts.