With a record number of female candidates running for president, some male Democratic contenders are signaling that a woman will be on their 2020 ticket — just not at the top.

Two male candidates, Senator Cory Booker of New Jersey and Beto O’Rourke, the former Texas congressman, suggested this weekend that they would pick a woman as their vice president if they won the nomination.

“It would be very difficult not to select a woman, with so many extraordinary women who are running right now,” Mr. O’Rourke told reporters in Iowa on Saturday night. But, he noted, “first, I would have to win, and this is as open as it’s ever been.”

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The packed Democratic field includes several prominent women, with Senators Elizabeth Warren, Kirsten Gillibrand, Kamala Harris and Amy Klobuchar all running competitively.