With the US supreme court apparently poised to overturn the 1973 landmark decision which made abortion legal, hundreds of thousands of people across America are planning to take to the streets to protest the looming decision.

A coalition of groups such as Planned Parenthood, UltraViolet, MoveOn and the Women’s March are organizing Saturday’s demonstrations, whose rallying cry is “Bans Off Our Bodies”. More than 370 protests are planned, including in Washington DC, New York, Los Angeles and Chicago.

The demonstrations come after the leak on 2 May of a draft opinion showing five conservatives on the nine-justice supreme court had voted to reverse their predecessors’ ruling in Roe v Wade nearly 50 years ago.

Unless the provisional ruling is changed substantially before becoming final, abortion would be outlawed essentially immediately in more than half of US states. People in those 26 states hostile to abortion would be forced to either travel hundreds of miles to a clinic in a state where terminating a pregnancy is legal or seek to self-administer an abortion through medication from grassroots or illicit groups.

While conservatives have celebrated the leak ruling, liberals have objected vociferously, gathering outside the supreme court building in Washington DC as well as the homes of some of the conservative justices to signal their displeasure.

Those rallies – generally peaceful – have been relatively small, while Saturday’s planned events will almost certainly be compared to the 2017 Women’s March the day after Donald Trump was inaugurated as president, which drew an estimated 3 million to 4 million participants across the US.

The “Bans Off Our Bodies” gatherings will take place three days after Democrats in the US Senate on Wednesday made a largely symbolic effort to advance legislation that would codify the right to an abortion into federal law. All 50 Republicans and one conservative-aligned Democrat – West Virginia’s Joe Manchin – voted against the measure, leaving it well short of the 60 votes necessary for it to advance.