Male candidates running for the 2020 Democratic presidential nomination have decided that the key to a woman’s political heart is committing to having a female running mate if he emerges as the party’s standard bearer.

Sen. Cory Booker of New Jersey and Rep. Eric Swalwell of California on Wednesday each pledged to name a woman as his vice presidential pick.

“Will I pledge to have a woman running mate?” Mr. Booker said Wednesday. “I will have a woman running mate. To me it is really clear that we [should] do that.”

The announcement comes as the men seeking the Democratic presidential nomination wrestle with the implications of running against women in a party that has seen a surge of female activism in the wake of President Trump’s victory over Hillary Clinton in 2016.

Democrats flipped control of the House last fall after voters elected a record number of women to Congress.

The previous year women — particularly black women — played an instrumental role in Sen. Doug Jones’ surprise 2017 special election win over Roy Moore in Alabama.

Mr. Booker made his vow Wednesday at the She the People presidential forum in Houston, which focused on the role women of color will play in the 2020 election.

“Remember we are a powerful voting bloc, one of five voters in primaries are women of color and we are 25% of the voters in key swing states — of Texas, South Carolina, Georgia, Florida, Arizona,” She the People President Aimee Allison told the crowd gathered to hear several of the presidential contenders. “We are also the strongest Democratic Party voters in Virginia, Pennsylvania, Ohio, Michigan and California.”

The 2020 field of presidential contenders have taken note.

“SPOILER ALERT: I’m a white man,” Mr. Swalwell tweeted late Tuesday. “I know where I can’t speak to someone else’s experience, and I pledge to (1) Pass the mic (2) Ask a woman to serve as VP.”

Mr. Swalwell linked to a clip from his Tuesday appearance with MSNBC’s Joy Reid, telling her, “I don’t think anyone’s identity should hold them back, but I think the next president should see all races, all identities.”

“I’ve pledged that I would ask a woman to serve as vice president,” he said. “I would put forward a diverse candidate.”

Last month, shortly after announcing his run, former Rep. Beto O’Rourke said he would likely pick a woman as a running mate.

“It would be very difficult not to select a woman with so many extraordinary women who are running right now,” he said. “But first I would have to win and this is as open as it has ever been.”

• S.A. Miller contributed to this report.

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