The head of the World Health Organization has said that access to safe abortions saves lives, after a leaked draft ruling indicated the US Supreme Court was mulling ending nationwide legal abortions.

Without explicitly mentioning the US case, WHO chief Tedros Adhanom Ghebreyesus warned that "restricting access to abortion does not reduce the number of procedures."

"It drives women and girls towards unsafe ones," he said in a tweet.

"Access to safe abortion saves lives."

His comments came amid a firestorm in United States, sparked by an unprecedented leak of a Supreme Court draft ruling, which suggested the court was poised to overturn the nationwide right to an abortion.

If the draft ruling is confirmed by the court, it would overturn the 1973 Roe v. Wade decision, which enshrined abortion rights across the country.

Abortion laws would then be left up to individual state legislatures, with as many as half expected to enact bans or new restrictions.

For many women, the potential loss of abortion rights across much of the United States raises the prospect of being forced to travel hundreds of miles for the procedure or giving birth in traumatic circumstances.

"Women should always have the right to choose when it comes to their bodies and their health," Mr Tedros said.

The UN health agency issued new guidelines on abortion care in March, in a bid to help protect the health of women and girls and prevent unsafe abortions.

What is Roe v Wade abortion ruling?

According to the WHO, around 25 million unsafe abortions are conducted around the world annually, with some 39,000 women and girls dying as a result each year, and millions more hospitalised due to complications.

Most of the deaths happen in lower-income countries, with Africa accounting for a full 60% and Asia for 30%, the data shows.

Protesters rallied under the slogan "off our bodies" in cities across the US last night, demanding abortion rights be protected.

Thousands of people turned out for an abortion-rights rally in New York City as Americans awoke to political and social upheaval, months before voters go to the polls in congressional midterm elections.

"I hope it inspires people to show up in the midterms and vote, and that's the one thing that I'm looking at as a positive," said 41-year-old Alaina Feehan, a talent manager in New York City, describing the moment as a "call to action".

Protests were held in US cities coast to coast, including Atlanta, Chicago, Denver, Los Angeles and Seattle, as the national Women's March organisation urged supporters to bring families and signs to "courthouses and federal buildings everywhere".

Demonstrators converged on the footpath just beyond the barricaded marble steps of the courthouse across from the US Capitol, voicing support for and opposition to ending a constitutional right to abortion nationwide.

Several dozen anti-abortion activists dominated the protests early in the day, beating on drums and chanting through megaphones: "Pro-choice is a lie, babies never choose to die," and "Abortion is violence, abortion is oppression."

Abortion rights advocates shouted back; "Off our bodies" and "abortion saves lives".

Anti-abortion demonstrators outside the Supreme Court in Washington

One sign displayed by a group identifying as Roman Catholics supporting abortion access said: "Thou shalt not steal my civil rights".

"I just feel that we're going backwards," Jane Moore, 64, said of the prospect that Roe, which legalised abortion nationally nearly 50 years ago, could be struck down. "It actually breaks my heart and makes me angry at the same time."

"It makes me very afraid. I feel very sorry for ... young women. You're starting all over again," Paula Termini, 70, a nurse who has worked in delivery rooms and Planned Parenthood clinics, told Reuters outside the court. "It's going to take a long time to get those gains back again."

The protests in Washington were a prelude to rallies planned by abortion rights advocates in cities across the country.

About 300 people gathered in downtown Atlanta just outside the city's Centennial Olympic Park yesterday evening, their chants in support of abortion rights drowned out by the din of honking horns from passing motorists.

"We will fight in these streets, we will fight in every street in America if we need to," said 19-year-old Wendy Nevarez-Sanchez, holding a "Hands off my uterus" sign.

Demonstrators outside the US Supreme Court in Washington

In the Los Angeles suburb of Pasadena, some protesters carried coat hangers, a grim reference to "back-alley" abortions that experts say could become common again in states where abortion is outlawed.

Addressing abortion-rights demonstrators in Seattle, Governor Jay Inslee declared; "Washington state is a pro-choice state and we're going to fight like hell to keep Washington a pro-choice state. That's why we're here today."

Perhaps the day's largest rally emerged in New York City, where at least 2,000 abortion-rights protesters assembled in lower Manhattan's Foley Square, waving signs with such slogans as "Bans Off Our Bodies" and "Abortion is Freedom".

Thousands of abortion rights activists gathered at Foley Square in New York

"I'm here standing up for my people. I'm here to say that reproductive justice is immigrant justice," said Diana Moreno, 34, pointing to how low-income women and the undocumented would be disproportionately affected by the loss of abortion rights.

A handful of demonstrators around Foley Square walked into the street and briefly blocked traffic.

In San Francisco, a man calling himself the "Pro-Life Spiderman" scaled a downtown skyscraper while posting video footage of his climb on Instagram.

Local news media reported that police took the man into custody.