AUSTIN, Texas (Reuters) - A bill to make enhanced airport security pat-downs a crime if they involve touching a passenger's private areas was approved by the Texas House on Monday.

The move came just days after the measure appeared dead when the House speaker called it "unenforceable" and "an embarrassment to the state of Texas."

Speaker Joe Straus asked lawmakers to revise the measure with the help of the Texas attorney general's office after Straus' comments sparked a firestorm from conservative and Tea Party activists who see the bill as a way to strike a blow against "federal government tyranny," as bill author Representative David Simpson -- like Straus a Republican -- has said.

Federal officials had threatened to halt all flights out of Texas airports if the original bill were passed on the grounds that they would not be able to certify that the flights were safe.

"We've been working with the attorney general's office from the very beginning to ensure that the bill will accomplish our goal of stopping the humiliation of travelers while also maintaining language that will withstand judicial scrutiny," Simpson said in a statement on Monday.

The major change in the amended bill, Simpson said, is a requirement that the Transportation Security Administration agent have "reasonable suspicion" before conducting an enhanced pat-down, a less stringent standard than the "probable cause" in the original measure.

The requirement to have probable cause before frisking an individual caused concern among Texas police officers, afraid it would make it more difficult to conduct routine searches of suspects -- and not just in airports.

"We're concerned about the entire jump to probable cause," said Charley Wilkison, the chief lobbyist for the Combined Law Enforcement Associations of Texas, which represents police organizations. "We're concerned about officers not being able to do their jobs."

The revised bill also includes a provision prohibiting the prosecution of a TSA officer if the officer's actions are "pursuant to and consistent with the Constitution." Violation of the law would be a Class A misdemeanor, punishable by up to a year in jail and a $4,000 fine.

Straus said he is now "satisfied with the House's efforts to pass legislation that lets Texans travel safely, protects the privacy of citizens, and enables law enforcement to do its job."

The measure died during the regular session of the legislature, which ended May 30, and Republican Governor Rick Perry added it to lawmakers' agenda for the special session, which ends on Wednesday. To make its way to Perry's desk, it needs one final vote from the House and approval by the Senate.

TSA officials have said on their blog that state may not regulate the federal government and that agents are "trying to work in partnership with the traveling public to make you safe on flights."

(Reporting by Jim Forsyth; Editing by Corrie MacLaggan and Jerry Norton)