Michael Dukakis won the endorsement of Sen. Joseph Biden, a one-time opponent who might have had grounds for a grudge, and struggled anew to come to terms with rival Jesse Jackson. Republican George Bush, meanwhile, expressed confidence that the "gender gap" will vanish once his views on the issues are known.

Bush was meeting at breakfast Thursday with Jeane Kirkpatrick, the former United Nations ambassador who is often mentioned as a potential running mate. The vice president has said he isn't yet considering specific candidates to fill his own job.However, some observers believe a woman on the ticket might boost Bush's support among female voters. A number of polls have suggested that women are far more likely to back Dukakis, the all-but-certain Democratic nominee, than Bush, his likely opponent. But the vice president dismissed such surveys.

"What you do is spell out your positions on the issues, and the gender gap goes away and you win the election," Bush told local reporters Wednesday on a trip to Louisville, Ky.

Bush, who has had to curtail his campaign travel to stay within federal spending limits, was spending today in Washington, with no campaign appearances planned.

Jackson, continuing to plot his convention strategy, had a morning meeting set in Washington with his campaign chairmen from 34 states. Then he was heading off on a three-day trip to what he called "the deep, deep South" - Puerto Rico, where he won a non-binding "beauty contest" primary earlier this year.

Despite that victory, Dukakis wound up with all 57 of the island's convention delegates. Jackson is likely to use the trip to point up what he considers to be inequities in the delegate-selection process, although his campaign has been quietly working with the Dukakis camp to resolve such disputes.