Speaking to reporters at a news conference, Paul said Gramm called him this week and told him, "You need to endorse McCain." The Texas congressman said he refused.
"The idea was that he would do less harm than the other candidate," Paul said.
Paul won no primaries in the Republican nomination contest but developed a strong following on the Internet.
He appeared at a news conference with three third-party candidates: independent Ralph Nader; former Georgia Democratic Rep. Cynthia McKinney, the Green Party candidate; and Chuck Baldwin, the Constitution Party candidate. Bob Barr, the Libertarian candidate, was invited but said at his own news conference later that he declined because Paul didn't endorse one candidate.
"We need today, now, 55 days before this election, bold, focused, specific leadership and that is not the amorphous kind that says any of the above or none of the above," Barr said.
Barr said he had asked Paul to join him as his running mate on the Libertarian Party ticket while his current running mate, Wayne Root would step aside. "We don't anticopate that he will," Barr said.
Earlier, Paul called the presidential elections a charade and said voters are faced with the "lesser of two evils."
The majority of Americans, about 60 percent, are unhappy with their choices in the race, Paul said. He urged the three third-party candidates to bring all their supporters together to vote against the "establishment candidates."
Paul, 73, a former doctor, ran for president as the Libertarian candidate in 1988. He is unopposed in the November race for his congressional seat.
Nader derided media focus on what he called "lipstickgate," referring to the bickering between the McCain and Barack Obama campaigns over whether a phrase used by Obama was a sexist comment against Republican vice presidential nominee Sarah Palin.
Nader, a consumer protection advocate, acknowledged differences among the third-party candidates such as government regulation of health and safety standards. But he added that he shares Paul's support for more opportunity in the political process for third-party candidates.