WASHINGTON — With the Republican Party in need of money for the November elections, former Mayor Rudolph W. Giuliani has offered to appear at fund-raisers around the country for G.O.P. candidates. But there is a catch: He wants some cash out of the deal.

Mr. Giuliani’s aides have told the National Republican Congressional Committee and Congressional candidates that if he makes an appearance, he wants the candidates to help him get rid of his presidential campaign debt.

The unusual request underscores the financial predicament Mr. Giuliani finds himself in, after he ended his presidential bid this year with roughly $3.6 million in campaign debt. Traditionally, prominent party figures help lower-tier candidates by headlining fund-raising events in return for good will and future political alliances, but do not receive funds themselves.