Mulvaney issued his statement after the president's outside legal counsel tried to distance itself from Mulvaney's earlier comments at a press briefing.
At an earlier briefing, Mulvaney had directly cited questions about the DNC server as a reason that money for Ukraine was being held up.
Trump, for his part, says he still has "a lot of confidence" in Mulvaney.
Mulvaney acknowledged at a White House press briefing Thursday that Trump's decision to hold up military aid to Ukraine was linked to his demand that Kyiv investigate the Democratic National Committee and the 2016 U.S. presidential campaign.
Later, Trump's personal attorney Jay Sekulow issued a one-sentence statement that said, "The President's legal counsel was not involved in acting chief of staff Mick Mulvaney's press briefing."
Mulvaney's comments raised questions at the Justice Department and brought swift rebuke from Democrats, who cast his words as an admission of wrongdoing. Mulvaney said Trump did nothing improper because he was asking for help investigating a prior election.
The chairman of the House Intelligence Committee says "things have just gone from very, very bad to much, much worse." Rep. Adam Schiff is referring to the White House's acknowledgement that it held up military aid to Ukraine while President Donald Trump pushed Ukraine's new leader to investigate Democrats.
Schiff is leading the Democrats' impeachment inquiry. Three House committees are investigating Trump's push to have the Ukrainian president conduct investigations that could benefit Trump's 2020 reelection campaign.
Schiff says the idea of withholding military aid is "a phenomenal breach of the president's duty to defend our national security."
Trump ultimately released nearly $400 million in military and other aid to Ukraine. And the president says he's done nothing wrong in his dealings with Ukraine.
The White House is acknowledging that President Donald Trump asked Ukraine's leader to investigate his country's role in meddling in the 2016 U.S. presidential campaign.
Trump's acting chief of staff, Mick Mulvaney, says Trump held up military assistance to Ukraine in part because of concern about corruption in that country.
Mulvaney says the administration also wanted Ukraine's cooperation in investigating whether Democratic National Committee's email servers were in Ukraine, and the White House was looking at levels of assistance that European nations were providing to Ukraine.
Mulvaney denies there was a quid pro quo and says "we do that all the time with foreign policy."
He points to the example of the administration holding up aid to Central American countries to force them to change their policies on immigration.
Trump ultimately released nearly $400 million in military and other aid to Ukraine.