By Jon Herskovitz

AUSTIN, Texas, May 21 (Reuters) - Texas governor Greg Abbott will sign in the next few days a bill that would shield ride-hailing firms Uber and Lyft from bruising battles over fingerprint background checks that led them to leave some of the state's most important markets.

Lawmakers last week approved the legislation known as House Bill 100 that sets up statewide regulations for the companies. It clears the way for Lyft Inc to reenter Houston, where Uber Technologies Inc currently dominates, and for both to reenter Austin, Corpus Christi and Galveston.

More than 40 states have set up statewide regulatory systems for ride-hailing companies such as Uber and Lyft that can be used to override local regulations in most places, according to the National Conference of State Legislatures.

"There is definitely a national, coordinated push from the industry to enact regulations for this type of transportation at the state rather than city level," said Lara Cottingham, deputy assistant director of administration and regulatory affairs for Houston, which opposed the state bill because it could supersede city regulations.

The Texas legislature on May 17 approved HB 100, a bill that eliminates local ordinances such as a fingerprint measure in Austin, which passed despite company objections and prompted the two firms to leave the Texas capital last year.

Also on May 17, lawmakers in Alaska, Louisiana and New York advanced legislation that also would take ride service regulations out of local hands.

Lawmakers in cities including Los Angeles, Chicago and San Francisco have argued that fingerprinting is needed for Uber and Lyft drivers. The companies say they already do comprehensive background checks, which make such measures unnecessary.

In Houston, the fourth most-populous U.S. city, Lyft left in 2014 over local ordinances including the fingerprint checks. Uber struck its own deal with local authorities to operate in Houston.

The Texas bill may also kill Houston regulations that ensure handicapped customers have access to services and customers can lodge complaints, officials said.

Mostly Republican backers of the bill said it benefits consumers by offering more choice and competition, which will drive down prices.

“A statewide framework for ridesharing will help bring greater economic opportunity and expanded access to safe, reliable transportation options to more Texans,” Sarfraz Maredia, general manager for Uber Texas, said in a statement.

CAUTIONARY TALE

In a 2016 election, Uber and Lyft spent more than $10 million in an unsuccessful effort to roll back city regulation. That exceeded the amount spent by all candidates running for mayor and city council in their most recent election.