Former CIA director retired Gen. David Petraeus arrives at Trump Tower talks with reporters after a meeting with President-elect Donald Trump, Monday, Nov. 28, 2016, in New York. (AP Photo/ Evan Vucci)

Former CIA director retired Gen. David Petraeus arrives at Trump Tower talks with reporters after a meeting with President-elect Donald Trump, Monday, Nov. 28, 2016, in New York. (AP Photo/ Evan Vucci)

NEW YORK (AP) — The drama, disputes and falsehoods that permeated Donald Trump’s presidential campaign are now roiling his transition to the White House, forcing aides to defend his baseless assertions of illegal voting and sending internal fights spilling into public.

On Monday, a recount effort, led by Green Party candidate Jill Stein and joined by Hillary Clinton’s campaign also marched on in three states, based partly on the Stein campaign’s unsubstantiated assertion that cyberhacking could have interfered with electronic voting machines. Wisconsin officials approved plans to begin a recount as early as Thursday. Stein also asked for a recount in Pennsylvania and was expected to do the same in Michigan, where officials certified Trump’s victory Monday.

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Trump has angrily denounced the recounts and now claims without evidence that he, not Clinton, would have won the popular vote if it hadn’t been for “millions of people who voted illegally.” On Twitter, he singled out Virginia, California and New Hampshire. In another series of tweets Monday, he lashed out at a CNN reporter who had called Trump’s fraud claim “baseless.”

There has been no indication of widespread election tampering or voter fraud in those states or any others, and Trump aides struggled Monday to back up their boss’ claim.

Spokesman Jason Miller said illegal voting was “an issue of concern.” But the only evidence he raised was a 2014 news report and a study on voting irregularities conducted before the 2016 election.

Trump met Monday with candidates for top Cabinet posts, including retired Gen. David Petraeus, a new contender for secretary of state. Trump is to meet Tuesday with Tennessee Sen. Bob Corker, who is also being considered more seriously for the diplomatic post, and Mitt Romney, who has become a symbol of the internal divisions agitating the transition team.

Petraeus said he spent about an hour with Trump, and he praised the president-elect for showing a “great grasp of a variety of the challenges that are out there.”

“Very good conversation and we’ll see where it goes from here,” he said. A former CIA chief, Petraeus pleaded guilty last year to a misdemeanor charge of mishandling classified information relating to documents he had provided to his biographer, with whom he was having an affair.

Trump is expected Tuesday to name Georgia Rep. Tom Price to lead the Department of Health and Human Services, said a person familiar with the decision, who insisted on anonymity because the person was not authorized to discuss the nomination publicly ahead of the announcement.

Vice President-elect Mike Pence, who is heading the transition effort, teased “a number of very important announcements tomorrow” as he exited Trump Tower Monday night.

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Pence is said to be among those backing Romney for State. Romney was fiercely critical of Trump throughout the campaign but is interested in the Cabinet position, and they discussed it during a lengthy meeting earlier this month.

Other top Trump allies, notably campaign manager Kellyanne Conway, have launched a highly unusual public campaign to warn the president-elect that nominating Romney would be seen as a betrayal by his supporters. Conway’s comments stirred speculation that she is seeking to either force Trump’s hand or give him cover for ultimately passing over Romney.

Three people close to the transition team said Trump had been aware that Conway planned to voice her opinion, both on Twitter and in television interviews. They disputed reports that Trump was furious at her and suggested his decision to consider additional candidates instead highlighted her influence.

Conway served as Trump’s third campaign manager and largely succeeded in navigating the minefield of rivalries that ensnared other officials. Trump is said to have offered her a choice of White House jobs — either press secretary or communications director. But people with knowledge of Conway’s plans say she is more interested in serving as an outside political adviser, akin to the role President Barack Obama’s campaign manager David Plouffe played following the 2008 election.

The wrangling over the State Department post appears to have slowed the announcements of other top jobs. Retired Gen. James Mattis, who impressed Trump during a pre-Thanksgiving meeting, was at the top of the list for Defense secretary, but a final decision had not been made.

Trump was also considering former New York City Mayor Rudy Giuliani for Homeland Security secretary, according to those close to the transition process. Giuliani was initially the front-runner for State and is still in the mix. But questions about his overseas business dealings, as well as the mayor’s public campaigning for the job, have given Trump pause.

Those close to the transition insisted on anonymity in commenting because they were not authorized to publicly discuss the private process.

Even as Trump weighs major decisions that will shape his presidency, he’s been unable to avoid being distracted by the recount effort. He spent Sunday on a 12-hour Twitter offensive that included quoting Clinton’s concession speech, in which she said the public owed Trump “an open mind and the chance to lead.”

His final tweets challenging the integrity of an election he won were reminiscent of his repeated, unsubstantiated assertions during the campaign that the contest might be rigged. Those previous comments sparked an outcry from both Clinton and some Republicans.

Clinton lawyer Marc Elias said the campaign has seen “no actionable evidence” of voting anomalies. But the campaign still plans to be involved in Stein’s recount to ensure its interests are legally represented.

Trump narrowly won Wisconsin, Pennsylvania and Michigan. All three would need to flip to Clinton to upend the Republican’s victory, and Clinton’s team says Trump has a larger edge in all three states than has ever been overcome in a presidential recount.

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Pace reported from Washington. AP writer Jon Lemire contributed to this report.

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Follow Julie Pace at http://twitter.com/jpaceDC and http://twitter.com/catherine_lucey