Senior Democrats have warned President Donald Trump not to use a controversial memo as a "pretext" to fire the special counsel probing alleged Russian involvement in the 2016 US election.

Democrats said the memo's release was a "shameful effort to discredit" the FBI and inquiries into Russian meddling.

They warned that such action could trigger a "constitutional crisis not seen since the Nixon era", the BBC reported.

The memo, written by Republicans, accused the FBI of abusing its powers.

Trump approved the declassification of the memo on Friday and said it "revealed a disgraceful story".

The memo focused on the court-approved wiretapping of Carter Page, a foreign policy adviser to the Trump campaign who was put under electronic surveillance by the FBI.

The memo accused the FBI and the Justice Department of using "unsubstantiated evidence" to obtain the October 2016 warrant.

It said that they did not tell the authorities their claim to the warrant was partially based on a dossier funded in part by the rival campaign of Hillary Clinton, the BBC report said.

It also said that the author of that dossier, a former British intelligence agent called Christopher Steele, told a senior Justice Department official that he was "desperate that Trump not win".

Democrats said the release of the memo was aimed at disrupting the probe into alleged links between the Trump campaign and the Kremlin.

Trump, who has consistently denied any such collusion, had in May 2017 even fired former Federal Bureau of Investigation Director James Comey over the probe.

Comey on Friday tweeted that the memo was "dishonest and misleading". The FBI said key facts had been omitted in the memo.

In a statement, Senate Minority Leader Chuck Schumer, House Minority Nancy Pelosi and eight other senior Democrats warned Trump against trying to sack special counsel Robert Mueller or Deputy Attorney General Rod Rosenstein.

"We write to inform you that we would consider such an unwarranted action as an attempt to obstruct justice in the Russia investigation," the statement said.

They said such action could result in a constitutional crisis not seen since the 1970s when then President Richard Nixon gave orders to fire justice officials involved in the Watergate scandal.

The White House later said "no changes" would be made at the Department of Justice and Rosenstein was fully expected to continue in his job.

Asked about the contents of the memo, Trump said a lot of people should be "ashamed of themselves".

Although Devin Nunes, who commissioned the memo, said it showed "serious violations" of public trust, not all Republicans supported the release of the memo.

Instead, Senator John McCain accused his party colleagues, and Trump, of playing into the hands of Russian President Vladimir Putin, The BBC reported.

"Our nation's elected officials, including the President, must stop looking at this investigation through the warped lens of politics and manufacturing partisan sideshows," he said in a statement.

"If we continue to undermine our own rule of law, we are doing Putin's job for him," Mccain said.