Mr. Biden has emphasized the need for a future Democratic president to work with Republicans, stressing the importance of consensus in order to get things done. That viewpoint has been criticized by some liberals who see it as an unacceptable embrace of the status quo and think Mr. Biden is naïve about trying to work with Republicans. But choosing a Republican to be his running mate would be a far more grievous act in the eyes of many Democrats, something many party officials and both liberal and moderate activists would oppose.

On Monday, Mr. Biden made a point of noting that it was presumptuous to talk about a running mate, given that he has not won the Democratic nomination. He went on to recall his working relationship with President Barack Obama and their trust for each other, telling the crowd, “The only thing I know about is the qualifications for vice president.”

As for his own vice-presidential pick, Mr. Biden noted that there were “a lot of qualified women” and “a lot of qualified African-Americans.”

“There’s a plethora of really qualified people,” he said. “Whomever I would pick were I fortunate enough to be your nominee, I’d pick someone who was simpatico with me.”

Mr. Biden, like other presidential candidates, has been largely circumspect about naming names, though he did say this month that he would consider a former rival in the race, Senator Kamala Harris of California, as a possible running mate. He also said that he would consider another primary rival, Senator Elizabeth Warren of Massachusetts.