In September, the White House published a transcript of Trump's July telephone conversation with Zelensky, during which he asked several times that his government investigate Biden, an incident that sparked the Democratic inquiry that could lead to the impeachment of the USA president.
"We have another transcript coming out which is very important", Mr Trump told reporters at Joint Base Andrews before leaving for a visit to Tuscaloosa, Alabama.
He added that this second transcript would probably be released on Tuesday. The House Intelligence, Foreign Affairs and Oversight committees sent Mulvaney a letter requesting he appear for a closed-door deposition as part of the Democrats' impeachment inquiry into Trump and Ukraine.
Mulvaney's request for the court to solve his dilemma comes as he has been clashing with one of the one of the president's other most senior aides, White House Counsel Pat Cipollone, over who should direct the president's response to the House impeachment inquiry, according to people familiar with the matter.
House investigators have released the testimony of Lt. Col. Alexander Vindman, a top specialist on Ukraine on the National Security Council.
Hill also is said to have told investigators that her then-boss, then-national security adviser John Bolton, also didn't want to go along with Trump's plan. "But this is the man who said there was no quid pro quo, and he still said that".
There were three words President Donald Trump wanted to hear from the Ukraine president: Investigations, Biden, Clinton.
Williams reportedly said that the tone of the call, which was political in nature, was not normal in comparison to other diplomacy calls.
Democrats suspect Trump may have withheld military aid from Ukraine to pressure the country to investigate corruption allegations against political rival Joe Biden.
Mr Trump on Friday objected to the public sessions, even though he, the White House and Republican allies, had objected to interviews taking place behind closed doors.
The inquiry was triggered by a complaint filed by a person who remains anonymous, though an alleged name has been reported in several media outlets.
A US House of Representatives Intelligence Committee official said that Bolton has threatened to take the committee to court if it subpoenas him. In recent cases related to the House impeachment inquiry, federal judges have repeatedly sided with the House, saying it should get what it has asked for.