Paul Manafort, the chairman of Donald Trump's presidential bid, has resigned, Trump said Friday as he continued steps to revamp his campaign team after weeks of controversy.

The move comes as part of a broader campaign staffing shake-up that earlier this week saw Trump bring a conservative media firebrand onboard as a top campaign executive and had left Manafort's role unclear.

Manafort has also drawn fire for millions of dollars in alleged undisclosed payments as part of lobbying efforts for a pro-Russian Ukrainian political party.

"This morning Paul Manafort offered, and I accepted, his resignation from the campaign," Trump said in a statement, adding that he appreciated his work. "Paul is a true professional and I wish him the greatest success."

The statement did not tie the resignation to either the broader campaign reorganization or the Ukrainian controversy.

Ukrainian anti-corruption authorities said Friday they were investigating Manafort over allegations related to his work on behalf of a pro-Russian political party.

Manafort "is among those names on the list of the so-called 'black ledger' of the Party of Regions," the Ukrainian National Anti-Corruption Bureau said in a statement.

The documents allegedly show funds allocated to Manafort totaling more than 12.7 million dollars between November 2007 and October 2012. But the agency emphasized that it had not determined whether he had actually received that money.

Although Manafort's work in Ukraine had been known, a New York Times article this month exposed the extent of his involvement, raised concerns about his financial compensation and fuelled questions about the campaign's possible pro-Russian sympathies.

Trump's son Eric Trump alluded to the concerns in a Fox News interview Friday, saying, "My father just didn't want to have the distraction looming over the campaign."

Democratic presidential candidate Hillary Clinton's campaign issued a statement about Manafort's resignation.

"You can get rid of Manafort, but that doesn't end the odd bromance Trump has with Putin," campaign manager Robby Mook said in a statement, noting Trump's praising of the Russian president.

Manafort's addition to the campaign earlier this year had been seen as bid to remake Trump's image to appeal to a broader sector of the electorate. He was also seen as key in running the final stages of the primaries and in steering it through the July party convention.

On Wednesday, Trump brought on board Stephen Bannon, the executive chairman of conservative news website Breitbart News, to serve as chief executive officer for the Trump campaign and promoted pollster Kellyanne Conway to campaign manager. It had been unclear how Manafort would factor into the new organization, though a statement on Wednesday said he was to remain on staff.

The reshuffle was seen as an acknowledgement that Trump wanted to double down on his campaign strategy and reject efforts by Manafort and others to remake his image.

Former campaign manager Corey Lewandowski, ousted from the campaign after a power struggle with Manafort, called the staffing changes "very important for the campaign" and told CNN that removing Manafort in favour of Bannon would allow Trump to be himself.

"Let's get back to allowing him to be authentic, to do what got him to where he is today," Lewandowski said.

Political observers have closely watched Trump for a change in tone, and Thursday evening he expressed uncharacteristic regret for his inflammatory choice of words in the past.

"Sometimes in the heat of debate, and speaking on a multitude of issues, you don't choose the right words or you say the wrong thing," he said at an evening rally in North Carolina.

"I have done that, and, believe it or not, I regret it."

Trump and vice presidential candidate Mike Pence toured flood-ravaged Louisiana on Friday.

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