(Attention to offensive language in paragraph 5)

MELBOURNE/SYDNEY, July 2 (Reuters) - Thousands of Australians joined raucous protests across the country on Saturday against the U.S. Supreme Court's overturning of women's constitutional right to abortion.

The Supreme Court last week overturned the landmark 1973 Roe v. Wade ruling, restoring the ability of individual states to ban abortion.

In the biggest rally in Australia, more than 3,000 women and men marched through Melbourne, with placards including "I borrowed this sign from my grandma," and "Everyone deserves the right to bodily autonomy".

"We are here to stand up for women's rights in Australia and around the world. Millions of women in the United States have had their rights stripped from them and we are angry about that," said Liz Walsh, one of the organisers of the protest in Melbourne.

The crowd chanted: "Fuck the church, fuck the state, women will decide their fate."

As in the United States now, in Australia, abortion laws are set by states. The country's most populous state, New South Wales, only legalised abortion in 2019 - the last state to do so.

The time limit after conception for accessing surgical abortion and provision of abortion services varies from state to state, with some providing more public health care access than others. South Australia bans private abortion clinics.

Protesters called for easier access across the country.

"I've come out today in solidarity with women and girls in America in protesting and advocating for their rights for choice and that abortion is healthcare and every woman deserves a right to that," said Melbourne protestor Geraldine Bilston. (Reporting by Sonali Paul in Melbourne and Stefica Nicol Bikes in Sydney; Editing by Lincoln Feast.)