The decision not to appeal by the Dallas-based firm of Rader, Campbell, Fisher & Pyke all but wraps up Jones' dispute with Mr. Clinton, who has said he is willing to comply with the court order issued Thursday by U.S. District Judge Susan Webber Wright.
"We thought that more attorneys fees were caused by his lying, but Judge Wright didn't see it that way and so it's over," lawyer Wes Holmes said Friday.
The head of The Rutherford Institute, a Virginia-based conservative group that also worked for Jones, said he likely would decide next week whether to appeal the institute's award, but would prefer to let the case end.
"We're weighing the money, the attorney time, the chance factor with the court and then probably as big of a factor: Do we want to be in this case for another year?" said Rutherford President John W. Whitehead.
The law firm had sought $437,825 and The Rutherford Institute had sought $58,533.
Mr. Clinton's attorneys have said the president will not appeal the $90,686 payment he was ordered to compensate for legal costs related to what the judge called his "false, misleading and evasive answers" in his January 1998 deposition.
There has been little reaction from either the White House or the president to the award, reports CBS White House Correspondent Mark Knoller. The president told CBS News that he expected the $90,000 award imposed on him by the judge.
The president's denials of a sexual relationship with Lewinsky led to his impeachment by the House. The Senate acquitted him after a trial.
Wright dismissed Jones' sexual harassment lawsuit April 1, 1998, but Mr. Clinton agreed to an $850,000 settlement after Jones appealed the dismissal. The president admitted no wrongdoing.
Despite the possible end to the case itself, a Supreme Court committee in Arkansas on professional conduct could still impose further sanctions against the president, including disbarment.