BEDMINSTER, N.J. (Reuters) - President-elect Donald Trump and 2012 Republican presidential nominee Mitt Romney set aside a fierce rivalry on Saturday and held talks likely to feed speculation that Romney could be in line to be the next U.S. secretary of state.

After a day of meetings, Trump emerged to tell reporters that his search process was going “really efficiently” and that he had spoken to “really, really talented” people who could form part of his Cabinet.

Trump said he might have some announcements on Sunday. He spoke highly of retired Marine General James Mattis, who transition officials said was a strong contender for defense secretary.

Earlier, Trump and Romney emerged from their meeting after an hour and 20 minutes, and Trump told reporters their talks “went great.” Romney said the pair “had a far-reaching conversation with regards to the various theaters in the world.”

“We discussed those areas, and exchanged our views on those topics – a very thorough and in-depth discussion in the time we had,” Romney said. “And I appreciate the chance to speak with the president-elect and I look forward to the coming administration and the things that it’s going to be doing.”

Trump’s team said in a statement that Trump and Romney held a “substantive and in-depth conversation about world affairs, national security and the future of America.”

“It was an extremely positive and productive conversation,” the statement said.

Trump met for an hour with Mattis. Asked if Mattis would be his defense secretary, Trump said, “He’s a great guy. He is some great man.”

The Trump team statement said Trump and Vice President-elect Mike Pence were “very impressed” with Mattis.

“They had an incredibly in-depth conversation on plans for national security. The discussion included ISIS, the Middle East, North Korea, China, NATO and other hotspots around the world,” the statement said.

Romney, who was a leader of the establishment Republican “never Trump” movement that tried to block Trump from becoming the nominee, was first in a long list of people Trump was meeting with on Saturday and Sunday as he seeks to fill out his Cabinet and gather advice ahead of his Jan. 20 move to the White House.

In March, Romney said Trump would be dangerous as president, with policies that could touch off a recession. Romney also said, “I’m afraid that when it comes to foreign policy he is very, very not smart.”

Trump had denounced Romney as a “choke artist” for losing the 2012 election to President Barack Obama.

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But with the New York real estate developer now president-in-waiting, Romney’s appearance at Trump National Bedminster on an unseasonably warm November day was symbolic of hard-won party unity.

‘SEAL OF APPROVAL’

Whether Romney will join the Trump administration is unclear. Romney, a more mainstream Republican, would serve alongside more hawkish Trump appointees named on Friday: Senator Jeff Sessions of Alabama as attorney general, retired Lieutenant General Michael Flynn as national security adviser and Representative Mike Pompeo as CIA director.

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Those nominations suggest Trump is setting up his administration to take a hard line confronting Islamist militancy and curbing illegal immigration.

Transition officials said Trump’s meeting with Romney was supposed to be a general discussion about the incoming administration.

A Romney confidant said of Romney’s secretary of state prospects: “Could it happen? I suppose. But it’s unlikely.”

Instead, the source said the meeting gives “the good housekeeping seal of approval to Republicans who don’t know if they should help Trump or not.”

Trump has been considering former New York Mayor Rudy Giuliani, a close adviser, for secretary of state, as well as former U.S. ambassador to the United Nations John Bolton and Senator Bob Corker of Tennessee. Trump is to meet Giuliani on Sunday.

Also on Saturday, Trump met with Andy Puzder, chief executive of CKE Restaurants, the fast-food giant that operates the Carl’s Jr. and Hardee’s chains. Afterwards, Trump said he was “getting very close” to making some Cabinet decisions.

Puzder, a possible labor secretary, said he would be “proud to serve in any position that this president asks me to serve in.”

In addition, he met with two candidates for education secretary: Michelle Rhee, the former Washington, D.C., public schools chancellor, and Betsy DeVos, a former head of the Michigan Republican Party.

On Sunday, Trump is to sit down with Wilbur Ross, a potential commerce secretary who made billions by investing in bankrupt companies and distressed assets, and business executive David McCormick, head of investment firm Bridgewater Associates, as well as New Jersey Governor Chris Christie, who was recently demoted in his role on Trump’s transition team.