In August the whistleblower filed a report that eventually triggered impeachment proceeding against Mr Trump.
Mulvaney was issued a subpoena Thursday and ordered to appear before the Intelligence committee Friday.
The battle is likely to go to the Supreme Court and could spill into next year.
They want to question Mulvaney about whether he was directly involved with President Trump's lawyer Rudy Giuliani to withhold almost $400 million in United States military aid to Ukraine.
Williams was one of a handful of U.S. officials who listened in on the call. A slew of current and former officials from the State Department and White House have appeared over the last several weeks and largely corroborated the same narrative - that Trump had delegated his lawyer, Rudy Giuliani, to guide U.S. -Ukraine policy and that the two men were focused on pressuring Ukraine as the administration withheld military aid from the country.
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She was later spotted at his Halloween party as well! 'They seemed to be enjoying each other's company, ' another source told the site.
President Donald Trump, when asked about Gordon Sondland's damaging testimony in the impeachment inquiry, claimed "I hardly know" his ambassador who gave a million to his inauguration. In an addendum to his testimony, Sondland said he now remembers a September conversation with Andrey Yermak, an aide to Ukraine's president, in which he "said that the resumption of USA aid would likely not occur until Ukraine provided the public anti-corruption statement that we had been discussing for many weeks".
Republicans have also accused Democratic House leaders of holding the inquiry in secret because they are closed-door, although Republican committee members have been present throughout.
Mulvaney's approach Friday marks a growing effort by top White House officials to stonewall the House and test their legal arguments in court as the House nears public testimony from witnesses regarding impeaching the President.
Three US diplomats who have already testified in private about their alarm about Trump's dealings with Ukraine will serve as star witnesses next week. Yovanovitch was ousted in May on Trump's orders and Taylor replaced her; both have testified about their concerns with the administration's policy on Ukraine.
"Williams testified that she had limited information about why military aid was being withheld from Ukraine".
Bolton defied the investigation Thursday by failing to appear for a deposition.