The issue of the memo has gripped Washington just as the Russia meddling probe edges closer to the White House.
Republicans are keen to see the four-page memo -- written by Republican lawmaker Devin Nunes, the chairman of the House Intelligence Committee and a close defender of Trump -- released, and his committee voted to do so.
After finishing his State of the Union address Tuesday night, Trump was caught on television cameras telling a Republican lawmaker who urged him to release it, "Don't worry, 100 per cent."
According to news reports citing people who have seen the document, it sums up how the Justice Department and FBI were able to obtain a so-called FISA national security warrant to run surveillance on Carter Page, a Trump election campaign advisor with extensive Moscow contacts.
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"There are legitimate questions about whether American civil liberties were violated by the FISA process," House Majority leader Paul Ryan said Tuesday.
"There may have been malfeasance at the FBI by certain individuals."
In addition, the memo alleges that after Trump became president, the warrant was extended by Deputy Attorney General Rod Rosenstein -- the DOJ official who appointed Mueller to lead the Russia probe, and the only person who can fire him.
Rosenstein took charge of the probe when Attorney General Jeff Sessions recused himself -- a move Trump has often criticized.
Democrats also say they cannot debunk it without themselves releasing top secret counterintelligence information.
The ranking Democrat on the House Intelligence Committee, Adam Schiff, said Monday the committee had "voted to put the president's personal interest, perhaps their own political interests above the national interest, in denying themselves even the ability to hear from the department and the FBI."
"That is, I think, a deeply regrettable state of affairs," said Schiff. All Democrats on the committee opposed the memo's release.