Lawmakers in Texas moved decisively on Thursday to curtail the distribution of mail-order abortion medications from states like New York and California, allowing nearly anyone to sue doctors, distributors and manufacturers anywhere in the country and collect cash awards.

Supporters hope and opponents fear the legislation, nearing final passage in Texas, will serve as a model for other states to limit medication abortion by promoting a rash of lawsuits against medical providers, pharmaceutical companies and companies such as FedEx or UPS that may ship the drugs.

If the legislation works as hoped, abortion opponents say, the availability of medication abortion could become more limited, even in states where abortion remains legal, because manufacturers and delivery companies could be expected to limit distribution in Texas to avoid legal liability.

“This is the strongest and the most legally dynamic attempt that our movement has made yet,” said John Seago, the president of Texas Right to Life. While the legislation is focused on Texas, he added, “hopefully this will lead to a wider protection.”