Trump has been dismissive of probes by the FBI and several congressional panels into alleged Russian meddling in the 2016 presidential election and potential collusion with his campaign, Reuters said.
In a series of early morning tweets, the president quoted a letter from Page, in which he asked to address the House Intelligence Committee promptly and referred to what he characterized as faulty testimony from U.S. intelligence officials.
Trump accused Democrats of blocking Page's testimony, without citing evidence but referring to an unidentified report.
"So now it is reported that the Democrats, who have excoriated Carter Page about Russia, don't want him to testify. He blows away their case against him & now wants to clear his name by showing 'the false or misleading testimony by James Comey, John Brennan...' Witch Hunt!" Trump wrote on Twitter, referring to the former directors of the FBI and CIA.
Trump's tweets came as his advisers are planning to establish a "war room" to combat mounting questions about communication between Russia and his campaign.
The White House said on Wednesday it would not answer any more questions about the investigations, referring reporters instead to Trump's outside attorney, Marc Kasowitz.
The president's penchant for tweeting could complicate White House efforts to tamp down the scandal if the messages appear to address the investigations.
Representative Adam Schiff, the top Democrat on the House committee, swatted back at Trump on Twitter with a reference to the president's acknowledgment to NBC that he was thinking of "this Russia thing" when he fired Comey on May 9.
"@POTUS, appreciate suggestion on witnesses but feel you may not have probe's interests at heart. Ex: Firing FBI Dir because of Russia probe," Schiff wrote.
Democrats say Comey's dismissal was aimed at hindering the Federal Bureau of Investigation's Russia investigation.
CNN reported on Wednesday that Comey would confirm reports that Trump had asked him to let up in an investigation of former White House national security adviser Michael Flynn's contacts with Russia in upcoming public testimony before the Senate Intelligence Committee.