The move came amid growing fears in the White House that the Democrats would be unable to muster the simple majority needed to defeat impeachment in the House and prevent a trial in the Senate.
Vice-President Al Gore, in his first comment since articles of impeachment - alleging perjury, obstruction of justice and abuse of power - were passed by the House judiciary committee on Saturday, called on Congress to censure rather than impeach.
Acknowledging that Mr Clinton's conduct in the Lewinsky affair was "terribly wrong", he told reporters at the White House: "There ought to be a censure, not impeachment." He condemned Republican leaders for "forcing this vote that the American people do not want".
Mr Gore said: "The vast majority of the American people have come to two conclusions about this whole matter: number one, what the President did was terribly wrong; number two, [they] have decided that ... he should not be impeached and removed from office as a result of that. What they favour instead is a censure to give the President the punishment and rebuke and censure that they feel is appropriate in this."
Democratic members of the House judiciary committee tried in vain last week to get a censure motion approved as an option for the full House debate. Senior Republicans have said they will oppose any attempt to revive the suggestion.
Within hours of Mr Gore's intervention, the White House special counsel, Gregory Craig, was also calling for censure as a reasonable way out. Mr Craig, who has fronted Mr Clinton's media defence in recent days, lentthe force of legal argument to the view that, while serious, the President's wrongdoing did not warrant removal from office.
Mr Clinton himself, meanwhile, speaking from Gaza shortly before delivering his historic address to the Palestinian National Assembly, reiterated his own readiness to accept a congressional reprimand. "I have offered to make every effort to make any reasonable compromise with the Congress," he told reporters. "And I still believe that. I'm willing to do that."
In a last-ditch attempt to stave off passage of the articles of impeachment last Friday, Mr Clinton had announced he was ready to accept a congressional rebuke or censure. But his remarks drew the ire of many Republicans who felt they were ill-judged and inappropriate. And on Sunday Mr Clinton took a different tack, ruling out resignation and insisting he would not admit perjury - "because I did not commit perjury".
Leading Republicans have stipulated that he must admit to lying under oath as the prelude to any compromise. But the White House sees the demand as a trap.
In his plea for a compromise yesterday, Mr Clinton set aside the rights and wrongs of the accusations against him and cited the national interest. "I don't believe it's in the interest of the United States and the American people to go through this impeachment process and have a trial in the Senate," he said.
However, telephone calls from Clinton aides to the 30 or so congressmen still undeclared ahead of Thursday's vote were said to be making little headway, while attempts to mobilise sympathetic business leaders to give warning of the risks to the national well-being from a Senate trial were written off as a failure.