(CNN) — The next stop in a legal battle over a controversial new abortion law in Texas could be the U.S. Supreme Court.
On Monday abortion-rights groups filed an emergency motion asking the Supreme Court to block Texas from enforcing part of the law, which is considered among the most restrictive in the country.
Justice Antonin Scalia has given the state until November 12 to respond, according to court documents.
The motion comes four days after a federal appeals court reinstated a key part of the law -- a provision that requires doctors to obtain admitting privileges at a hospital within 30 miles of the clinic at which they're providing abortion services.
The appeals court's decision allowed that provision to remain in place, but Monday's motion asks the Supreme Court to overturn that ruling.
Since the decision, more than a third of centers that had provided abortions in Texas have stopped providing abortions, Louise Melling, a deputy legal director of the American Civil Liberties Union, told reporters in a conference call Monday.
"A dozen abortion providers were forced to cancel appointments immediately," said Kenneth Lambrecht, director and CEO of Planned Parenthood of Greater Texas. "Our patients are scared, some are angry, some have said they don't know how they're going to make the long trip to the next closest provider."
Marni Evans, 37, a freelance consultant, told reporters she is now considering flying to Seattle for an abortion after her appointment in Austin, Texas, was canceled.
She said she and her fiance decided to pursue an abortion for financial reasons.
"We can barely afford our own health care, let alone a child, she said. "After a lot of soul searching, we decided we want to start a family someday, but we just can't do it right now. Because of last Thursday's ruling, that decision has been taken out of our hands."
A Planned Parenthood lawsuit against the state over the law is still pending. The suit -- filed in U.S. District Court in Austin on behalf of more than a dozen women's health care providers across Texas -- alleges that the abortion law violates the constitutional rights of women and puts unreasonable demands on doctors who perform abortions.
The bill originally failed to gain approval because of a Democratic filibuster led by state Sen. Wendy Davis.
Gov. Rick Perry then called the Legislature into a second special session to continue consideration of the bill.
Perry cheered last week's appeals court ruling.
"Today's decision affirms our right to protect both the unborn and the health of the women of Texas," he said in a statement last week. "We will continue doing everything we can to protect a culture of life in our state."