Biden meanwhile railed at "extremist" and "cruel" Republicans in a speech at the White House marking the 51st anniversary of Roe v Wade, the landmark judgment legalizing abortion that the conservative-leaning US Supreme Court then stunningly overturned in in 2022.
Harris and Biden warned that Republicans will impose a nationwide abortion ban if the party wins the November presidential election.
Already, 21 states have brought in full or partial bans since the Supreme Court -- where three Trump-appointed justices tilted the balance sharply to the right -- issued its ruling.
"These extremists are trying to take us backwards. We are not having it," Harris, 51, said to a cheering crowd in Big Bend in Wisconsin, which is expected to be one of the most closely fought states in this year's election.
Democrats increasingly see the issue as a vote winner after Trump repeatedly said he was "proud" and took credit for the end to a federally protected right to abortion.
"Proud? Proud that women across our nation are suffering? Proud that women have been robbed of a fundamental freedom?" she said. "How dare he?"
Women attending the rally said the messages from Harris and Biden were "important."
"I don't know that there's any laws that regulate what a man can do with his body, so why is a man trying to tell a woman what she should be able to do with her body?" Corinda Rainey-Moore, a community outreach organizer, told AFP.
- 'Cruelty is astounding' -
Irene Parthum, a retired former district attorney, said she supported the Democrats' stance because of "my daughter and hopefully her daughter someday. I want them to have the same rights I had."
The Supreme Court decision has left millions of American women without access to abortion. Fourteen US states have imposed outright bans on abortion since the ruling, while seven others have imposed time limits.
The Biden campaign has launched a blitz on the issue this week, seeing it as a potential weakness for Trump in particular as he heads for a likely rematch against Biden.
Meeting his reproductive rights task force at the White House, Biden repeatedly described the Republicans as "extreme" on abortion.
"The cruelty is astounding," Biden said.
"Today, in 2024, in America, women are turned way from emergency rooms, rooms, forced to travel hundreds of miles to get basic healthcare," Biden said.
He called abortion bans in cases of rape or incest as "outrageous," and highlighted life sentences for doctors in Texas who carry out abortions, and plans in Alabama to prosecute people who help others cross state lines for terminations.
The White House's focus on abortion rights continues on Tuesday when Harris and Biden will make their first joint appearance on the 2024 campaign trail with a major rally in Virginia on Tuesday.
The Biden campaign said it was also launching television and social media ads targeting swing voters in battleground states, focusing on the "personal impact that Trump's abortion bans have on women."
The issue remains a seismic fault line in US politics and society.
Polls repeatedly show a clear majority of Americans support continued access to safe abortion, even as conservative groups push to limit the procedure -- or ban it outright.
Biden is a devout Catholic but in recent years the 81-year-old has taken on the role as the defender of women's reproductive freedoms.
Harris is meanwhile increasingly becoming the campaign's face on the abortion issue, giving her an opportunity to combat low approval ratings and attacks by Republicans on her fitness as first-in-line to the presidency.
