The calls evinced the spread of concern in Washington that the scandal was imperilling the Presidency.
The most striking and forceful appeal came from Senator Orrin Hatch, who is chairman of the Senate Judiciary Committee, which has the power to impeach the President. Speaking on a succession of television talkshows, he said that full disclosure by the President, even if it entailed an admission of perjury, could end the threat of impeachment.
"If he comes forth and tells it and does it in the right way and there aren't a lot of other factors to cause the Congress to say this man is unfit for the presidency and should be impeached, then I think the President would have a reasonable chance of getting through this," he told the NBC programme, Meet the Press.
"I don't know anybody at the top of the system," he said, "who really wants to see the President hurt in this matter."
Mr Hatch's carefully worded plea, which was endorsed by other senior Republicans, offered mercy for Mr Clinton, but on the express condition that his one crime was to have lied about his relationship with Ms Lewinsky in the evidence he gave to prosecutors in the civil sexual harassment suit brought by Paula Jones.
Legal specialists noted, however, that any indulgence shown towards Mr Clinton raised many legal questions: would perjury then be permissible, if it was about sex or motivated by a desire to save one's family?