Abortion rights protesters have rallied in cities around the United States, vowing to fight to ensure terminating a pregnancy remains a legal option for women nationwide.

Hundreds gathered in Chicago, Atlanta, Houston and other cities days after a draft US Supreme Court opinion was leaked to the public suggesting the court is poised to overturn the landmark 1973 Roe v Wade case that legalised abortion nationwide.

The draft opinion, which comes after nearly 50 years of federal abortion protections, could change before the ruling is finalised in coming weeks.

"To think that, after all this time, people still want to control what women can do and our rights to make our personal healthcare decisions is just really outrageous," Carole Levin, chair of Courts Matter Illinois, told WMAQ-TV during the rally in Chicago.

Illinois Governor J.B. Pritzker attended the rally and vowed to protect reproductive rights in Illinois.

"I'm proud Illinois is an island for reproductive freedom in the midwest," he said.

"Our shores remain open for any person left marooned by these extremist politicians."

In the nation's capital, abortion rights protesters stood outside the Supreme Court, holding signs that said abortion is a human right, and "Abort the Court."

Protesters who oppose abortion demonstrated across the street.

In Atlanta, demonstrators carried signs in favour of abortion rights as they marched through that city's downtown and chanted, "Not the church and not the state, women must decide our fate".

In Houston, thousands attended a reproductive rights rally headlined by Democrat Beto O'Rourke, who is running for Texas governor.

Texas is one of several states that would automatically ban abortion, leaving no exceptions for rape or incest, if the high court overturns the nationwide right to abortion.

An investigation is underway to determine who leaked the Supreme Court draft opinion to reporting outlet Politico.