AUSTIN, Tex. — Texas Democrats tried to prevent Republicans from passing a bill on Tuesday that would give the state some of the toughest abortion restrictions in the country, even as Gov. Rick Perry appeared ready to keep lawmakers in town to give the bill another chance.

The bill would ban abortions after 20 weeks of pregnancy, require abortion clinics to meet the same standards that hospital-style surgical centers do, and mandate that a doctor who performs abortions have admitting privileges at a nearby hospital.

Supporters of the bill, including the governor and other top Republicans, said the measures would protect women’s health and hold clinics to safety standards, but women’s rights advocates said the legislation amounted to an unconstitutional, politically motivated attempt to shut legal abortion clinics. The bill’s opponents said it would most likely cause all but 5 of the 42 abortion clinics in the state to close, because the renovations and equipment upgrades necessary to meet surgical-center standards would be too costly.

On Tuesday, the Senate took up a version of the bill that the House had passed the day before. But the 30-day special session of the Legislature expired at midnight and there was confusion about whether a Senate vote passing the bill was legitimate.