Alone among the justices, Clarence Thomas said he would have granted Trump's request to keep the documents on hold.
Trump's attorneys had asked the high court to reverse rulings by the federal appeals court in Washington and block the release of the records even after President Joe Biden waived executive privilege over them.
In an unsigned opinion, the court acknowledged there are "serious and substantial concerns" over whether a former president can win a court order to prevent disclosure of certain records from his time in office in a situation like this one.
But the court noted that the appeals court determined that Trump's assertion of privilege over the documents would fail under any circumstances, "even if he were the incumbent".
It said the issue of a former president's ability to claim executive privilege would have to wait for another day.
The court took issue with the conclusion of the appeals court that downplayed a former president's interests, suggesting that the current president could in essence ignore his predecessor's claims.
Justice Brett Kavanaugh, who worked in the White House under President George W. Bush, wrote separately to argue that "a former President must be able to successfully invoke the Presidential communications privilege for communications that occurred during his Presidency, even if the current President does not support the privilege claim".
But Kavanaugh, a Trump appointee, did not object to the outcome Wednesday.
Before and after the riot, Trump promoted false theories about election fraud and suggested the "real insurrection" was on Election Day, when he lost to Biden.
Repeating arguments they made before lower courts, Trump's attorneys had urged the justices to step in, arguing that the case concerned all future occupants of the White House. Former presidents had "a clear right to protect their confidential records from premature dissemination", Trump's lawyers said.
"Congress cannot engage in meandering fishing expeditions in the hopes of embarrassing President Trump or exposing the President's and his staff's sensitive and privileged communications 'for the sake of exposure'," they added.
But the House committee responded in its high court brief that although the facts of the case are "unprecedented", the decision was "not a difficult one".
There was no explanation for the timing of the court's action. But the National Archives told the appeals court and Trump's lawyers that it would turn over some documents it asserted were not part of the court case on Wednesday absent a new court order.
Also on Wednesday, the House committee investigating the Capitol insurrection issued subpoenas to leaders of an alt-right group who appeared at events promoting baseless claims of voter fraud after the 2020 election.
The committee demanded records and testimony from Nick Fuentes and Patrick Casey — internet personalities who have promoted white supremacist beliefs — regarding what lawmakers say is their promotion of unsupported claims about the election and their presence on Capitol grounds on January 6.
Since its creation last summer, the committee has interviewed almost 350 people as it seeks to create a comprehensive record of the attack and the events leading up to it.
- Associated Press writer Farnoush Amiri contributed to this report.
