President-elect Donald Trump held a surprise media briefing Tuesday in the lobby of his Trump Tower residence in New York City and said he has a full day of meetings with people as he continues the vetting process for positions in his administration, including secretary of state, the nation's top diplomatic post.
"We have a lot of people coming up. Great group of people. Doing very well," Trump said.
Vice President-elect Mike Pence said earlier Trump is "taking his time" to select a secretary of state. "The role of secretary of state, the person that's going to be representing the president overseas and with countries around the world is a unique role," Pence said during an interview on MSNBC's "Morning Joe."
Also speaking Tuesday, Trump spokesman Jason Miller said Trump wants to make sure "he's getting this important pick right" and wants someone who has "the same vision for what we are trying to do for the country."
Trump has already met with numerous candidates for the position, including former critic Mitt Romney. Romney is reportedly the leading contender for secretary of state, while former New York City Mayor Rudy Giuliani is said to be falling out of favor.
Among those the president-elect is scheduled to meet with is ExxonMobile Corporation CEO Rex Tillerson, who has been mentioned as a candidate for secretary of state. The 64-year-old Texas oil man has no government experience and has close ties with Russian President Vladimir Putin and other world leaders. His appointment could raise conflict of interest concerns because of his financial holdings in Exxon, which explores oil and gas throughout the world and has operations in more than 50 nations.
Trump appeared last week to have narrowed his list to four names: Romney, Giuliani, former Central Intelligence Agency chief David Petraeus and Tennessee Senator Bob Corker. But he also interviewed former U.N. Ambassador John Bolton and is talking to several others as well, including retired Navy Admiral James Stavridis and former U.S. Ambassador to China Jon Huntsman.
The president-elect will also meet Tuesday with former Secretary of State Henry Kissinger, Iowa Governor Terry Branstad, radio talk show commentator Laura Ingraham, and Washington Mayor Muriel Bowser.
Washington Mayor Muriel Bowser, right, boards an elevator at Trump Tower in New York, Dec. 6, 2016.
The billionaire real estate mogul, meanwhile, took to Twitter to announce he wants to the cancel an order for a new Air Force One, the plane that flies presidents throughout the world. The government has contracted with the Boeing Company to construct at least two new planes, which would go into service in 2024.
The planes initially cost about $3 billion, but the costs have reportedly been rising, Trump tweeted “the costs are out of control”.
WATCH: Trump comment to reporters about Boeing
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Trump Slams Boeing for Pricey Air Force One Upgrade
Boeing responded to Trump's criticism of the the rising costs, saying in a statement that the contract is for $170 million, not the "more than $4 billion" included in Trump's tweet.
"We are currently under contract for $170 million to help determine the capabilities of these complex military aircraft that serves the unique requirements of the President of the United States," the statement said.
The statement from the aerospace giant suggested that the project is simply in one of several phases that must be completed during the development and building process. "We look forward to working with the U.S. Air Force on subsequent phases of the program allowing us to deliver the best planes for the President at the best value for the American taxpayer."
The president-elect will fly later to Fayettville, North Carolina, when he will formally announce retired General James Mattis as secretary of defense. Fayetville is home to Fort Bragg, the largest military base in the world.
Protests, Vote re-count
Early Tuesday outside Trump Tower, supporters of a three-state vote recount joined Green Party presidential candidate Jill Stein in a rally to ensure an “accurate, secure, and fair” vote.
“We are here to assure Donald Trump that there is nothing to be afraid of,” said Stein. “If you believe in democracy, if you believe in the credibility of your victory, put down your arms, end your bureaucratic obstruction, end your intimidation and join we the people of America who are calling for a democracy that serves all of us and elections that we can trust."
WATCH: Related report by Ramon Taylor
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Anticipation Builds for Final Cabinet Picks at Trump Tower
Protesters interrupted and taunted the group of supporters with shouts and signage. “Illegal voting, far left crybabies, Stein will not change outcome: President Trump on January 20, 2017!!” read one woman’s sign.
A judge has ordered a hand recount begin in Michigan, one of three battleground states that Stein believes may have been hacked due to aging voting machines. Similarly, she is pushing for a federal court order to enact a recount in Pennsylvania.
Ramon Taylor and White House correspondent Mary Alice Salinas contributed to this report