Gov. Robert F. McDonnell is backing off his unconditional support for a bill requiring women to have an ultrasound before an abortion, focusing new attention on one of the most controversial pieces of legislation in Virginia’s General Assembly this year.

Until this weekend, McDonnell (R) and his aides had said the governor would sign the measure if it made it to his desk. McDonnell, who strongly opposes abortion, will no longer make that commitment.

But delegates and governor’s staff were scheduled to meet Tuesday night to strike a compromise after learning that some ultrasounds could be more invasive than first thought, according to two officials who were aware of the meeting but not authorized to speak about it publicly. Many of the bill’s supporters were apparently unaware of how invasive the procedure could be, one of the officials added.

The Virginia legislation has become part of the broader national debate over reproductive rights and has drawn attention to McDonnell, a rising star in his party and a possible vice presidential contender. The legislation has been the topic of cable news shows, was part of a “Saturday Night Live” sketch and drew protesters to Richmond on Monday.

McDonnell’s office would say Tuesday only that the governor will “review” the bill if it is approved.

“Our position is: If the General Assembly passes this bill the governor will review it, in its final form, at that time,” McDonnell spokesman Tucker Martin said in a statement. He declined to explain the change in approach, but Virginia’s governors can sign, veto or amend legislation.

The House and Senate have approved their versions of the bill. On Tuesday, the House postponed a final vote on the legislation— as well as votes on other measures on guns and adoption — for the second day in a row.

“Something is happening,’’ Jessica Honke, a lobbyist for Planned Parenthood Advocates of Virginia, said hopefully. “It’s important for [the governor] to take a long, hard look before he actually does this.”

In recent days, abortion supporters have emphasized that women in the earliest stages of pregnancy may require a probe instead of an external test.

About 1,200 men and women held a silent protest outside the state Capitol on Monday, wearing hand-decorated T-shirts that bore such messages as “Virginia is for lovers, not probes.’’

Opponents of the measure expect to turn over petitions with 25,000 signatures on Wednesday and are planning a second rally on Thursday.

In the past week, the issue has been featured on left-leaning shows, including “The Rachel Maddow Show” and “PoliticsNation with Al Sharpton.” And “The Daily Show with Jon Stewart” arrived in Richmond on Tuesday to film.

The legislation is being used against Republicans outside of the General Assembly. National and state Democrats have criticized U.S. Senate candidate George Allen for his anti-abortion stand and have derided McDonnell, who has hit the campaign trail for presidential hopeful Mitt Romney.

Republicans at the Capitol, however, remain optimistic that McDonnell will sign the measure.

“The governor is strongly pro-life, and I think he would hold consistent in his support for this bill,” said Del. Ben L. Cline (R-Rockbridge), co-chairman of the Conservative Caucus.

Republicans, in control of the General Assembly since last month, have other abortion-related bills pending during the 60-day legislative session.

Bills ending state subsidies for low-income women to abort fetuses that have serious birth defects and giving rights to a fertilized egg at the moment of conception are working their way through the legislature.

Del. Lionell Spruill Sr. (D-Chesapeake) took to the House floor Tuesday to say: “I’m deeply disappointed in some of you. I can’t believe you would disrespect women in this county, in this state.”

The ultrasound legislation would require women to undergo a test to determine the gestation age of the fetus, hear the heartbeat and be given an opportunity to see the images.

A woman who refuses to look at the ultrasound would have to sign a statement, which along with a print of the image would become part of her medical file.

The bill also would require women who live within 100 miles of their abortion provider to wait at least 24 hours before having the procedure, except in emergencies. Those who live farther would have to wait two hours.

Supporters of the ultrasound measure say it would provide crucial medical information to women seeking abortions; opponents say it would subject women to unnecessary tests and invade their privacy.

It is unclear whether insurance companies would cover the procedure.

Democrats hope to alter the bill on Wednesday to make the ultrasound voluntary.

“There is no doubt that this bill . . . is fundamentally and seriously flawed,” Del. Charniele Herring (Alexandria) told her colleagues. “It is time to end the shame that has been brought to Virginia and to this chamber by this extreme bill.’’

The officials with knowledge of Tuesday night’s Republican meeting said GOP leaders hope to introduce amendments on Wednesday, but it is unclear whether the rank and file would support them.

McDonnell, who signed legislation last year that imposed new regulations for abortion clinics, first said last month that he would sign the ultrasound bill. His position was reiterated by his press secretary, Jeff Caldwell.

Victoria Cobb, president of the conservative Family Foundation, which considers the ultrasound bill one of its top priorities, said Tuesday that she and her staff were trying to determine what they need to do to persuade the governor to sign the legislation.

“It is a change as far as I can tell,” she said of McDonnell’s shift.

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