US abortion-rights campaigners, including several Democrats running for president in 2020, rallied in front of the supreme court and across the country on Tuesday to protest against extreme new restrictions on abortion passed by legislatures in eight states.

According to the website #StoptheBans, about 400 events were set to take place across all 50 US states.

Some of the new laws recently passed by Republican state legislatures amount to the tightest restrictions on abortion seen in the United States in decades. Alabama passed an outright ban last week, including for pregnancies resulting from rape or incest, unless the woman’s life is in danger.

Hundreds of abortion rights supporters rallied for nearly two hours outside the supreme court, applauding fiery speeches from senators, members of Congress, activists and six presidential candidates who made clear the issue is likely take centre stage in the 2020 election.

Cory Booker, Kirsten Gillibrand, Amy Klobuchar, Seth Moulton, Tim Ryan and Eric Swalwell, all competing to be the Democratic presidential candidate, described the anti-abortion drive as an attack on human rights and an attempt by Trump-emboldened Republicans to turn back the clock. Another candidate, Pete Buttigieg, mayor of South Bend, Indiana, was also in attendance but did not make remarks.

The mood among the crowd in bright sunshine was defiant, energetic and hopeful. Protesters waved signs saying, “We won’t be punished” and “Protect Safe, Legal Abortion”. A small counter-demonstration also took place.

“We are not going to allow them to move our country backward,” Klobuchar, senator from Minnesota, told the crowd through a megaphone. “You know who’s with us? The American people are with us.”

The rally is one of scores being organized by the American Civil Liberties Union, Planned Parenthood Action Fund and other civil rights groups, in what they are describing as a Stop Abortion Bans Day of Action.

One of the most powerful speeches of the day came from congresswoman Ayanna Pressley of Massachusetts. “I am outraged because this is outrageous,” she said. “This nation was built on the backs and grown in the wombs of women and our rights are not up for debate.”

Among those in attendance outside the supreme court was Kathy Kleeman, 66, from South Brunswick, New Jersey. She said: “For all women in this country, it’s essential we protect these rights. I remember before Roe v Wadeand it wasn’t good: it was very spotty and dangerous for a lot of women, and we mustn’t go back to that.”

She added: “Right-wingers are in the ascendant. I don’t believe Donald Trump cares about the issue one way or another, but this is red meat for his supporters.”

Gillibrand, senator from New York, said Trump is turning women into “second-class citizens” in America. “This is the beginning of President Trump’s war on women. If he wants this war, he will have it and he will lose.”

Booker, senator from New Jersey, said: “We must wake up more men to join this fight and it’s not because we have mothers and wives and daughters. But because this is an assault on human dignity, on freedom.”

Warning of the danger of apathy, Booker added that current generation cannot rest on the laurels of what previous generations achieved for civil rights. “This is a day in America when we must understand there can be no neutrality … Today is a day in our land when we see people trying to take us backwards, but we must go forwards.”

Ryan, congressman from Ohio, acknowledged that he used to be “pro-life” but, having worked with politicians and advocacy groups, and heard the stories of women, he had changed his position. “I find it insulting that some white male legislator is going to accuse women of infanticide and not caring about these kids.”

Many of the restrictions are intended to draw legal challenges, which religious conservatives hope will lead the nation’s top court to overturn the 1973 Roe v Wade decision that established a woman’s right to make the choice on whether to terminate a pregnancy.

Other states, including Ohio and Georgia, have banned abortions absent a medical emergency after six weeks of pregnancy or after the fetus’s “heartbeat” can be detected, which can occur before a woman even realizes she is pregnant. At six weeks an embryo is neither a fetus nor has a recognizable heart.

Those laws are in defiance of the Roe v Wade ruling, which affords a woman the right to an abortion up to the moment the fetus would be viable outside the womb, which is usually placed at about seven months, or 28 weeks, but may occur earlier.

Several speakers in front of the supreme court argued that Congress must take action to codify Roe v Wade into law. Leaders of Naral Pro-Choice America and Planned Parenthood also addressed the gathering.

The bans have been championed by conservatives, many of them Christian, who say fetuses should have rights comparable to those of infants and view abortion as tantamount to murder. The supreme court now has a 5-4 conservative majority following two judicial appointments by Donald Trump.

Civil rights groups are suing to overturn the bans as eroding a woman’s right to bodily autonomy and say they endanger women who seek riskier illegal or homespun means to terminate a pregnancy.

On Tuesday, nearly two dozen states and municipalities sued the federal government to stop a new rule letting health care clinicians object to providing abortions and other services that conflict with their moral or religious beliefs.

The lawsuit filed in Manhattan federal court asked a judge to block a rule by the Department of Health and Human Services that is scheduled to take effect in July.