(CNN) A top White House official said on Thursday that President Donald Trump had withheld nearly $400 million in military aid to Ukraine in order to pressure the country to open an investigation that he thought would politically benefit himself, worrying some Republicans in Congress in the middle of an impeachment inquiry.

Mick Mulvaney, the acting White House chief of staff, told reporters that the Trump administration "held up the money" for Ukraine because the President wanted to investigate "corruption" in Ukraine related to a conspiracy theory involving the whereabouts of the Democratic National Committee's computer server hacked by Russians during the last presidential campaign. When pressed on whether the President sought an exchange of favors, Mulvaney said, "We do that all the time with foreign policy."

It was the first time the White House acknowledged a link between the withheld aid and probes that Trump sought.

Some Republicans were deeply concerned by Mulvaney's comments.

"You don't hold up foreign aid that we had previously appropriated for a political initiative," said GOP Sen. Lisa Murkowski of Alaska. "Period."

Republican Rep. Francis Rooney of Florida called Mulvaney's acknowledgment about withholding Ukraine aid "troubling," saying it is "not a good thing" to do that in connection "with threatening foreign leaders."

Rooney would not rule out the prospects of supporting impeaching the President.

"I'm not going to say anything about that until all the facts are in," he said. "I remember too many people saying, 'Oh, this is a witch hunt against Richard Nixon,' and come to find out it wasn't a witch hunt."

Hours after the news conference, Mulvaney released a statement reversing his prior comments, now claiming there was "absolutely no quid pro quo between Ukrainian military aid and any investigation into the 2016 election."

"The President never told me to withhold any money until the Ukrainians did anything related to the server," he added.

Over the past few weeks, Republicans on Capitol Hill have defended the President, claiming there was no quid pro quo between Trump and Ukraine.

Rep. Mark Meadows of North Carolina said on Thursday that he had not yet seen Mulvaney's comments. "To date, every single witness, every single fact has not supported any pause or holdup on foreign aid being attached to any conditions," he said.

The Democrats' impeachment proceedings are focused on a July 25 call in which Trump asked Ukrainian President Volodymyr Zelensky to do him a "favor" and "find out what happened" with a Democratic National Committee server that had been hacked by Russians during the 2016 presidential campaign, according to a reconstructed transcript released by the White House. Trump has suspected that it is hidden in Ukraine, a false claim shared by right-wing conspiracy theorists.

Trump has repeatedly questioned the US intelligence community's finding that the Russians hacked and disseminated materials in support of his campaign.

The Department of Justice is investigating the origins of its investigation of Russian interference in the election. A senior Justice Department official told CNN, "If the White House was withholding aid in regards to the cooperation of any investigation at the Department of Justice, that is news to us."

The Democrats' impeachment inquiry has been more focused on a separate ask the President made on that now-famous call, for an investigation into former Vice President Joe Biden and his son Hunter, who sat on the board of a Ukrainian energy company, Burisma Holdings, whose owner had been probed by the former Ukrainian general prosecutor. There is no evidence of wrongdoing by either Joe or Hunter Biden.

Rep. Mac Thornberry of Texas, the top Republican on the House Armed Services Committee, criticized the President's conduct on Thursday, telling CNN that it was "inappropriate" but not "impeachable."

Democrats have said the President abused his power, seeking political and personal gain from his public office. They said Mulvany's comments only provided further confirmation of the central allegation of the probe, first laid out in a government whistleblower complaint publicly released in September, that Trump used the presidency to solicit foreign interference in the 2020 election.

Democratic Rep. Ted Lieu of California said Mulvaney's comments were "very damning" for Trump.

"Mick Mulvaney today on national TV says yes, there was a quid pro quo essentially on the DNC conspiracy theory investigation," Lieu said. "That is all very damning for the President of the United States."