Idaho has become the first US state to pass an abortion ban modeled after a controversial Texas law that prohibits abortions after about six weeks or when a heartbeat is detected.

The news comes with abortion rights under assault across the US – despite clear majority support for such rights. The conservative-dominated US supreme court is thought likely to overturn Roe v Wade, the 1973 ruling which established the right, later this year.

On Monday, Idaho house members passed the ban 51-14. No Democrats supported the legislation. The Senate has approved the bill and the Republican governor, Brad Little, is expected to sign it.

Abortion rights groups called on Little to use his veto.

Planned Parenthood called the bill a copycat of the Texas bill that became law last May and was controversially left in place by the supreme court.

“Idaho’s anti-abortion lawmakers ignored public opinion and rushed through this legislation, looking to capitalize on the US supreme court’s failure to block Texas’s ban,” Planned Parenthood said, adding that the bill’s proponents have been open about wanting Idaho to become “the next Texas”.

Jennifer M Allen, chief executive of Planned Parenthood Alliance Advocates, an Idaho nonprofit, said: “Little must do the right thing, listen to the medical community and veto this legislation before it forces Idaho patients to leave the state for critical, time-sensitive care or remain pregnant against their will.”

The Idaho bill would also allow family members to sue doctors who perform procedures after six weeks of pregnancy, before most people know they are pregnant. The bill provides a minimum reward of $20,000 plus legal fees within four years of the abortion for successful suits, compared to minimum $10,000 and legal costs under the Texas law.

Unlike the Texas law, the Idaho bill provides some exceptions in cases of rape or incest. While a rapist could not sue practitioners under Idaho’s new bill, family members could. Victims would have to file a police report and provide it to a doctor before they could get the procedure.

“This bill is not clever, it’s absurd,” said Democratic representative Lauren Necochea, adding that the rape and incest exemptions were “not meaningful”.

Last year, Little signed a “heartbeat” bill into law, but it included a “trigger provision” that stopped it being in effect until a federal court approved it, which has not happened.

Several Republican-run states have taken steps to restrict abortion rights. Among them, bills in Missouri would permit lawsuits against those who help someone cross state lines to get an abortion. Terminating non-viable pregnancies would be a criminal offense.

The Oklahoma senate recently passed six anti-abortion measures, including a copycat of the Texas ban. In February, the Arizona senate passed an abortion ban that would prohibit the procedure after 15 weeks, similar to the law passed in Mississippi, which is expected to lead the supreme court to overturn Roe v Wade.