WASHINGTON—President Trump ordered the declassification of sensitive documents related to the investigation into Russian election interference, a move that could eventually allow the public unprecedented access to a probe that he has repeatedly railed against.

The declassification order pertains to FBI transcripts, text messages and other law-enforcement and intelligence material related to an active investigation into some of the president’s closest advisers.

Mr. Trump has repeatedly denounced the investigation as a “witch hunt” and he and his allies in Congress have sought to undermine its legitimacy by painting it as politically motivated and tainted by bureaucratic abuse—an accusation that senior Justice Department officials have repeatedly denied.

The White House said the president made the decision in response to requests from members of Congress and to further public transparency. Legal experts and former government officials said the move represented an extraordinary level of presidential involvement in an investigation that has notched guilty pleas from five of Mr. Trump’s associates.

Mr. Trump on Monday ordered that more than 20 pages of a federal warrant used to obtain a secret wiretap on one of his former advisers, Carter Page, be declassified, as well as all Federal Bureau of Investigation interviews that went into obtaining the warrant.