Updated at 3:39 p.m.

North Carolina Gov. Pat McCrory (R) said Wednesday that he will veto an abortion restrictions bill moving through the state legislature unless his administration's concerns are addressed.

Within hours of that threat, state House Republicans pressed forward on the matter, passing less-restrictive abortion requirements through a committee. Supporters say the new language addresses McCrory's concerns.

McCrory has criticized the way the bill was brought up in the state Senate last week -- at the last minute and tacked on to another unrelated measure -- but also says he agrees with many of the bill's provisions. State Department of Health and Human Services Secretary Aldona Wos on Tuesday expressed concerns about other aspects of the bill, though, and urged the state House to take its time.

"Unless significant changes and clarifications are made addressing our concerns that were clearly communicated by DHHS Secretary Aldona Wos, Gov. Pat McCrory will veto the existing bill, HB 695, if it is passed by the House and Senate," the governor's office said in a statement.

His office added: "The governor would like to thank those members of the legislature who have been working with the administration to ensure that the bill’s goals and objectives are clearly to protect the health and the safety of women. The governor believes that major portions of the bill are of sound principal (sic) and value."

The measures passed through the state Senate last week would require abortion providers to meet strict licensing standards that most don't currently meet and would require doctors to be present throughout the abortion procedure. Abortion opponents say the new rules ensure safer procedures, while abortion-rights advocates say they are aimed at shutting down abortion providers.

State House Republicans on Wednesday morning added similar language to a motorcycle safety act and passed it through committee by a 10-5 vote. But House Speaker Thom Tillis (R) said the full House wouldn't vote on it Wednesday, according to reports.

Supporters note that the new state House measure alters some of the more controversial components of the state Senate bill. It would only require a doctor to be present when the first drug is administered in a chemical abortion, and would not reduce requirements for abortion providers, as compared to the state Senate bill, the News and Observer reports.

It's not clear yet whether the updated legislation meets McCrory's requirements to avoid a veto.

"The governor needs to hear from his team first," McCrory spokesman Ryan Tronovitch said.

During his 2012 campaign, McCrory said that he would not sign into law any further restrictions on abortion.

Republicans in the state legislature could technically override any veto from McCrory, as both chambers have the three-fifths majorities necessary. But overriding the veto of a governor of your own party would be highly unusual.

North Carolina is just the latest state to move toward restricting abortion. Several other states have limited the window during which women can obtain abortions and placed new restrictions on abortion providers.

Just last week, GOP governors in Ohio and Wisconsin signed new abortion restriction measures into law.