Abortion rights supporters began gathering for protests across the United States on Saturday, starting what organizers said would be "a summer of rage" if the US Supreme Court overturns the Roe v. Wade case that legalised abortion nationwide.

Planned Parenthood, Women's March and other abortion rights groups organised more than 400 "Bans Off Our Bodies" marches for Saturday, with the largest turnouts expected in New York City, Washington, Los Angeles and Chicago.

The demonstrations are in response to the May 2 leak of a draft opinion showing the court's conservative majority ready to reverse the 1973 landmark decision that established a federal constitutional right to terminate a pregnancy.

The court's final ruling, which could give states the power to ban abortion, is expected in June. About half of US states could ban or severely restrict abortion soon after a ruling vacating Roe.

Organisers said they anticipated hundreds of thousands of people to participate in Saturday's events, which they said would be the first of many coordinated protests around the Supreme Court's decision.

"For the women of this country, this will be a summer of rage," said Rachel Carmona, president of Women's March. "We will be ungovernable until this government starts working for us, until the attacks on our bodies let up, until the right to an abortion is codified into law."

Democrats, who currently hold the White House and both chambers of Congress, hope that backlash to the Supreme Court decision will carry their party's candidates to victory in congressional elections in November.

Students for Life of America, an anti-abortion advocacy group with campus chapters across the country, said it was holding counter protests on Saturday in nine cities, including in Washington. (Reuters)