Trump has been dismissive of investigations by the Federal Bureau of Investigation and several congressional panels into alleged Russian meddling in the 2016 presidential election and potential collusion with his presidential campaign.
In a series of morning tweets, the Republican president quoted a Monday letter from Page in which he asked to address the House Intelligence Committee promptly and referred to 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 early morning tweets came as his advisers are planning to establish a "war room" to combat mounting questions about communication between Russia and his presidential campaign before and after November's election.
However, the president's penchant for tweeting could complicate White House efforts to tamp down the scandal if the messages appear to address the investigations.
Fellow Republicans, including Senate Majority Leader Mitch McConnell, have urged Trump to tweet less and more wisely. U.S. Representative Sean Duffy said the Russia investigations were becoming too much of a distraction in Trump's 4-month-old presidency.
"I think the president should step aside from any comments, any tweets on the investigation and focus on the agenda that he ran on," Duffy said on CNN on Wednesday. "Stop tweeting about it, stop talking about it and get about the business of your agenda."
Republicans control both the Senate and the House of Representatives.
Page, who provided a copy of his letter to Reuters, said the committee postponed an appearance scheduled for next week without giving a specific reason.
House Intelligence Committee representatives said on Wednesday the panel does not make communications public and would not comment on Page's remarks.
Page, a businessman who worked in Russia at U.S. investment bank Merrill Lynch, advised Trump during his presidential campaign.
Russia has denied U.S. intelligence agencies' conclusion that Moscow interfered in the election campaign to try to tilt the vote in Trump's favor. The president has denied any collusion.
Congressional committees have contacted a parade of Trump associates and advisers, as well as former White House officials, to request information in their probes.
They include former national security adviser Michael Flynn, Trump, former campaign manager Paul Manafort, former press officer Boris Epshteyn, personal lawyer Michael Cohen and informal adviser Roger Stone.