He said he can not endorse such a "categorical and limitless assertion of presidential immunity from judicial process".
"The only truly absolute about presidential immunity from criminal process is the Constitution' s silence about the existence and contours of such an exemption", he wrote.
Vance began his probe after federal prosecutors in NY completed their investigation into payments that Trump's former personal lawyer, Michael Cohen, arranged to be made to the two women to keep them silent during the presidential race.
The U.S. Court of Appeals for the Second Circuit in NY granted the motion due to "the unique issues raised by this appeal", which had been filed by Trump's lawyers in the morning seeking an answer by 1 p.m.
The president is separately trying to block Deutsche Bank AG from handing over financial records, which the bank has said include tax returns, sought by committees of the U.S. House of Representatives.
U.S. District Judge Victor Marrero in the Southern District of NY ruled that withholding the taxes could "frustrate the administration of justice" in regard to President Trump's conduct.
For just about a NY minute, prosecutors in that state were set to get their hands on eight years' worth of President Trump's tax returns.
Mr Trump's lawyers immediately filed an emergency appeal with a higher court. "A thing like this has never happened to any President before".
Cohen is now serving three years in prison after admitting paying hush money - in violation of campaign finance laws - to Ms Daniels and another woman, tax fraud, and lying to Congress.
Trump's lawyers have said the investigation is politically motivated and that the quest for his tax records from January 2011 to the present should be stopped because he is immune from any criminal probe as long as he is president. "I'm not the one that slept with the porn star", Cohen told The New Yorker in an exclusive interview before he went to prison in May. That dispute is also before the federal appeals court. The Trump Organization later reimbursed Cohen.
Federal prosecutors are barred from charging a sitting president with a crime because the Justice Department has decided that presidents have temporary immunity while they are in office. The lawyers acknowledged that their argument had not been tested in courts, but said the release of the president's tax returns would cause him "irreparable harm".
Even if the returns are eventially turned over to the grand jury, it does not necessarily mean that they will be made public, as investigative materials typically are sealed.