Walter F. Mondale, saying he had "called President Reagan's bluff" on Social Security, today challenged Reagan to promise no reductions in Medicare and dismissed the president's claim that Mondale looked better in Sunday's debate because he wore makeup.

"That's the same answer that Nixon gave when he debated Kennedy," Mondale told a boisterous crowd of more than 10,000 at a noontime rally here. "Mr. President, the problem isn't makeup on the face. It's the makeup on those answers that gave you a problem."

Mondale, buoyed by one of the biggest crowds of his campaign, also countered Reagan's lighthearted challenge that the two candidates have an arm wrestling match, which Reagan suggested Tuesday to resolve questions about his age.

"We had a little brain wrestle on Sunday night, didn't we?" Mondale joked. "And in the next debate a week from Sunday, when we debate foreign policy, he'll find that the issue that worries Americans is not arms wrestling but the need for arms control."

Mondale also responded to charges by Reagan today that he has "made a career out of weakening" America's defenses. "I have always been for a strong defense," he said, "and as a matter of fact, I am confident that under a Mondale administration it would be stronger."

Turning the argument back on Reagan, he said a strong defense cannot be built from "a $7,000 coffeepot," or when "you ignore the role of arms control . . . , fail to get your allies to do their share . . . and spend billions on weapons that don't work."

Mondale's challenge on Medicare, the federal health care program for the elderly, came as he continued to hammer Reagan on the "fairness issue." That theme is central to Mondale's efforts to unify Democrats in key industrial and agricultural states and sustain his post-debate momentum.

"The mission is to capitalize on the excitement and to bring those states into line as we get national movement in the polls," a senior campaign strategist said today. "We are on the verge of a major breakthrough if we can have a good Ferraro debate and maintain our momentum."

Vice President Bush and Rep. Geraldine A. Ferraro are scheduled to debate at 9 p.m. Thursday in Philadelphia.

After his rally in Pittsburgh, Mondale flew to New York, where he met with Israeli Prime Minister Shimon Peres.

Mondale's challenge on Medicare came one day after he accused Reagan of having a "secret plan" to cut Social Security benefits if reelected, especially for future retirees. Hours later, Reagan said he would not cut benefits for current and future retirees.

That pledge took him beyond his debate statement, which made no mention of future beneficiaries. But Mondale questioned the validity of the president's latest statement, noting that Reagan had made a similar preelection promise in 1980.

"The question is, which Reagan do you believe?" Mondale asked his audience today. "The Reagan who for four years tried to undermine Social Security . . . or the Reagan who once again, four weeks before the election says, 'Oh, I'm all for you again?' "

Today, Mondale accused Reagan of planning "to increase the cost that old folks must pay when they're ill. His proposal would raise the average cost of a hospital stay by $1,500. If Mr. Reagan is reelected, his leaders are talking about converting it into a welfare program . . . .

"Mr. President," Mondale said, "I demand -- the American people demand -- tell us right now before the election whether you're going to continue to go after Medicare, undermine the support for seniors, or whether you will pledge to support that program."

Mondale has been greeted by increasingly enthusiastic crowds this week, and his strategists hope that will close the margin between him and Reagan.

Between now and the time he cuts back his campaign schedule to prepare for the Oct. 21 debate in Kansas City, Mondale must shore up his political base in the industrial and agricultural heartlands.

Mondale trails Reagan in all six states where he is campaigning this week. The latest Washington Post-ABC News polls found him 13 points behind here in Pennsylvania, 7 points behind in New York, 11 in Ohio, 14 in Michigan, 28 in Wisconsin and 11 in his home state of Minnesota.

Together, those states have 124 of the nation's 538 electoral votes. It takes 270 electoral votes to win the presidency. Next week, Mondale will make a final pre-debate swing up the Pacific Coast.

After his meeting with Peres, Mondale planned to attend a Democratic fund-raiser.