The move comes after the United States Supreme Court's decision on Friday to overturn the landmark Roe v. Wade ruling which recognized a woman's constitutional right to an abortion and legalized it nationwide.

"For all women, for human rights, we must engrave this acquired right in stone," Borne wrote on Twitter. "The Parliament must be able to rally very strongly around this bill."

Her comment came a day after French President Emmanuel Macron said abortion was a "fundamental right for all women."

The issue is being thrust onto the French political stage at a time when the country is grappling with the challenge of a highly fragmented parliament.

Aurore Berge, leader of the Renaissance party in the National Assembly, said the party would draft a law proposal to add abortion rights to the French constitution.

"In France we guarantee and advance the rights of women. We protect them," she said on Twitter. "As of today, with my Renaissance group, we are tabling a constitutional bill to protect access to abortion."

Macron is under pressure to build compromises in France's parliament after a stinging election defeat last week which resulted in a loss of his absolute majority.

The president has since sought to reach out to political opponents, asking them to come up with ideas for the fragmented parliament to legislate.

Parliament deputy Philippe Ballard, of the far right party Rassemblement National, said his party had no intention to seek to overturn abortion rights in France.

"We don't touch the Veil law," he told the France Inter radio station, referring to France's abortion rights legislation.

He said his party had voted against a proposal to extend the right to abortion to 14 weeks from 12 weeks of pregnancy.

The Veil law, allowing abortions up to 10 weeks of pregnancy, was adopted in France in 1975. It extended to 12 weeks in 2001 and then to 14 weeks in March this year.

(Reporting by Nicolas Delame and Mimosa Spencer; Editing by Mike Harrison)

By Nicolas Delame and Mimosa Spencer