LUBBOCK, Texas (AP) - The only abortion clinic in a 300-mile swath of West Texas can resume taking appointments Tuesday, after a federal judge struck down new restrictions that would have effectively shuttered it and at least a dozen other clinics across the state. Lubbock's Planned Parenthood Women's Health Center had stopped making appointments last week, bracing for this week's scheduled enforcement of a new requirement that all doctors performing abortions in the state must have admitting privileges at a hospital less than 30 miles away. Supporters who sued to block the requirement, part of a broad series of abortion limits the Legislature approved in July, argued it was meant to outlaw abortions, not make them safer as state officials had claimed. The judge agreed, finding that the law imposed an unconstitutional burden on women seeking to terminate a pregnancy. The admitting privileges provision "does not bear a rational relationship to the legitimate right of the state in preserving and promoting fetal life or a woman's health and, in any event, places a substantial obstacle in the path of a woman seeking an abortion," Judge Lee Yeakel, an appointee of President George W. Bush, a former Texas Republican governor, wrote in his decision. The non-descript brown Lubbock clinic, often targeted by protesters, performs abortions only on Thursdays, when a doctor flies in from East Texas to perform them. Clinic officials said the 30-mile limit would effectively end abortions at the facility. Abortion rights supporters argued most hospitals will not grant abortion doctors admitting privileges for religious, business or competitive reasons. As a result, they said, the law would shut down about a third of the 38 clinics in Texas. "I don't see why local hospitals would give privileges to someone who's not going to admit patients," said Beth Shapiro, chairwoman of the board of directors of Lubbock's center. She said hospitals have to conduct yearly reviews to keep accreditation up to date. Why go through those procedures if the providers aren't using the hospital? Shapiro said. "I have no doubt that this case is going all the way to the United States Supreme Court," Abbott said during a stop in Brownsville, Texas, as part of his campaign to replace retiring Gov. Rick Perry. The law also threatened to stop abortions at both clinics in Fort Worth and two of the five clinics in neighboring Dallas County, said Danielle Wells, spokeswoman for Planned Parenthood of Greater Texas. Those clinics had continued to make appointments, but had warned that they might be canceled because of the law. The abortion law will likely take center stage in the Texas gubernatorial campaign. Abbott is adamantly anti-abortion and opposes the procedure even in cases of incest and rape. Abbott's likely opponent, if he wins the 2014 Republican nomination, is Democrat state Sen. Wendy Davis, who gained national attention for a nearly 13-hour filibuster that temporarily stalled passage of the law in the Republican-controlled Legislature. "As a mother, I would rather see our tax dollars spent on improving our kid's schools rather than defending this law," she said in a statement following the ruling. In another part of his ruling, Yeakel partially blocked the provision requiring doctors to follow an 18-year-old U.S. Food and Drug Administration protocol. Abortion rights supporters complained that requiring doctors to follow the FDA's original label for an abortion-inducing drug would deny women the benefit of recent advances in medical science. Associated Press reporters Christopher Sherman in Brownsville and Nomaan Merchant in Dallas contributed to this report. Follow Chris Tomlinson on Twitter at http://twitter.com/cltomlinson .