(CNN) -- The Oklahoma Senate voted Tuesday to override the governor's vetoes and pass two strong anti-abortion measures.

One law requires women to undergo an ultrasound examination and listen to a description of what it shows before getting an abortion.

Senate President Pro Tempore Glenn Coffee, a Republican, said Tuesday's vote shows lawmakers listened to Oklahoma's residents and "made a bold statement in support of the sanctity of life." But Democratic Gov. Brad Henry has called the legislation "an unconstitutional attempt by the Oklahoma legislature to insert government into the private lives and decisions of its citizens."

Henry vetoed the bill and another abortion-related measure Friday, but the state House on Monday overwhelmingly voted to override both vetoes, with House Speaker Chris Benge, a Republican, lauding his colleagues for moving quickly. The Senate's 36-12 vote Tuesday was the final step required to make the bills laws

"Those who rallied behind this cause reflected the core values of Oklahoma citizens, and I applaud my colleagues in providing more safeguards for the life of the unborn," Coffee said.

Henry said he was disappointed by Tuesday's vote.

"It signals the beginning of another costly and possibly futile legal battle for the state of Oklahoma. Both laws will be challenged and, in all likelihood, overturned by the courts as unconstitutional," he said. "I fear this entire exercise will ultimately be a waste of taxpayers' time and money."

In a statement issued after his vetoes Friday, Henry sharply criticized the laws.

"State policymakers should never mandate that a citizen be forced to undergo any medical procedure against his or her will, especially when such a procedure could cause physical or mental trauma," Henry said. "To do so amounts to an unconstitutional invasion of privacy."

Henry said one of the flaws of the ultrasound bill was that it lacked an exemption for rape and incest victims.

Henry vetoed similar legislation in 2008. His veto was overridden. The State Supreme Court struck down the legislation because it contained multiple subjects, a violation of the state Constitution requiring measures to deal with a single subject, Bennett said.

The Center for Reproductive Rights said it had filed a lawsuit challenging the new law after Tuesday's Senate vote.

"Oklahoma has now passed the most burdensome ultrasound law in the country," Nancy Northup, the organization's president, told CNN. "Until Oklahoma stops harassing women who are seeking abortions, we will continue to sue the state on these unconstitutional restrictions."

Coffee said challenging the new laws in court would go against what Oklahoma residents want.

"The voice of the people has spoken twice now this session in the Senate and twice in the House, and I sincerely hope those who would reverse the people's voice would think twice before acting," he said.

The other measure approved by legislators Tuesday prohibits pregnant women and their families from seeking legal damages if physicians "knowingly and negligently" withhold key information or provide inaccurate information about their pregnancies.

Henry, in opposing the bill, said it would be "unconscionable to grant a physician legal protection to mislead or misinform a pregnant woman in an effort to impose his or her personal beliefs on his patient."

Such an issue would be particularly relevant to fetuses with disabilities.

"By prohibiting recovery of damages in wrongful birth and life malpractice actions, the legislation would allow unscrupulous, reckless or negligent physicians to knowingly withhold information or negligently provide inaccurate information to pregnant women without facing the potential of legal consequences," the governor said.

The House voted to override the veto of the ultrasound bill by an 81 to 14 vote, well above the three-fourths majority required. State Rep. Lisa Billy, a Republican, said the bill "does nothing more than give women as much information as possible before they make the life-altering decision to have an abortion."

"I don't want a single woman to go through the lifelong torture of having an abortion without having all the relevant information," Billy said.

The House voted 84 to 12 to override the veto over the legal damages prohibition. State Rep. Dan Sullivan, a Republican, said the bill "simply states that a doctor cannot be sued based on the opinion after birth that a child would have been better off if he or she had been aborted."

"A bipartisan coalition of members supported this bill the first time, and I am pleased they did again today," Sullivan said.

Benge, the House speaker, said, "We must move to stop the degradation of human life seen in recent years and stand up for those who cannot defend themselves."

CNN's Joe Sterling and Catherine E. Shoichet contributed to this report.