Pro-choice campaigners in Albuquerque, New Mexico were celebrating after they soundly defeated a ban on late-term terminations.

Voters in a municipal election rejected the measure by 55 per cent to 45 per cent on Tuesday despite an emotional campaign that brought in national anti-abortion groups and hundreds of thousands of dollars' worth of advertising.

The campaign compared abortion to the Holocaust and displayed pictures of aborted foetuses.

A coalition of rights groups, including the American Civil Liberties Union of New Mexico and Planned Parenthood, called the results a huge victory for Albuquerque women and families.

"Albuquerque families sent a powerful message - they do not want the government interfering in their private medical decisions," said Micaela Cadena of the Respect ABQ Women campaign.

"Dangerous, unconstitutional laws like the one we rejected have no place in Albuquerque, no place in New Mexico, no place anywhere in our nation."

Albuquerque became the focus of the campaign because it is home to Southwestern Women's Options, one of just a handful of US clinics that perform late-term abortions.

The proposal would have banned abortions after 20 weeks except to save the mother's life.

But, elsewhere, a sharply divided Supreme Court allowed the state of Texas to continue enforcing restrictions that have forced more than a third of the state's clinics to stop providing abortions.

Supreme Court justices voted 5-4 to leave a provision which requires doctors who perform abortions in clinics to have admitting privileges at a nearby hospital.

The court's conservative majority refused the plea of Planned Parenthood and several Texas abortion clinics to overturn a preliminary federal appeals court ruling that allowed the provision to take effect.

The four liberal justices dissented.

The case remains on appeal to the 5th US Circuit Court of Appeals in New Orleans.

That court is expected to hear arguments in January and the law will remain in effect at least until then.