SAN JOSE — In an admission of defeat, city leaders are backing off strict rules for ride-booking companies they adopted months ago that had left Silicon Valley with just about the only major airport where passengers couldn’t choose Uber over Yellow Cab.

In June, the city adopted rules requiring drivers for ride-booking companies to submit fingerprints and meet vehicle-age requirements before picking up passengers at the airport, a bid to appease the more heavily regulated traditional taxi companies, who complained of unfair competition. But Lyft and Uber denounced the regulatory scheme, and no drivers for the ride-booking companies agreed to sign up. “We determined the program wasn’t something ride-share companies were interested in, so we knew we had to go back to the drawing board,” said Rosemary Barnes, spokeswoman for Mineta San Jose International Airport.

The City Council on Tuesday will consider eliminating mandatory fingerprints for all drivers, replacing it with random monthly audits of 1 percent of the drivers. The audits would verify the driver’s identity, review their criminal history and look for any outstanding warrants.

The California Public Utilities Commission, which regulates the ride-booking as well as limousine and shuttle companies, requires background checks for drivers. But cities may establish the rules for ground transportation at their airports.

The monthly auditing process, a model that’s been used in San Diego, would include random curbside audits using mobile fingerprinting equipment.

“It makes it a little more feasible and less onerous on everybody,” Barnes said. “We recognized the San Diego model may very well work for our airport.”

Ride-booking giants Uber and Lyft had protested the rules San Jose adopted in June that went into effect in September, calling them unusual and overburdening. Not a single ride-booking company applied for a permit to operate at San Jose’s airport. And no other major California airport requires fingerprints from ride-booking drivers like what San Jose had asked for in June, including Oakland, San Francisco or LAX.

“The previous pilot program had requirements in place that would put a burden on individual drivers,” said Lyft spokeswoman Chelsea Wilson. “We like this new plan and believe it’s a way forward.”

Mayor Sam Liccardo had fought hard to fingerprint all ride-booking drivers, saying the safety of San Jose residents lies in his hands and citing examples of cases in which Uber drivers with violent prior offenses caused injury or death.

But he now supports the monthly random audit program used in San Diego, as long as it’s done by an accredited firm and the ride-share companies pay for it. His recommendations drew support from Vice Mayor Rose Herrera, and councilmen Raul Peralez, Don Rocha and Johnny Khamis.

Cabbies say Liccardo, who vowed not to compromise on fingerprinting, caved to political pressure from outside groups, including longtime friend Carl Guardino, the CEO of the Silicon Valley Leadership Group. The group has been pushing San Jose leaders to back off the rules for Uber and Lyft drivers, drafting a letter with signatures of 93 Silicon Valley CEOs. Guardino’s wife is a lobbyist for Lyft.

“From what I’ve seen, the only entity that’s been pushing this is Silicon Valley Leadership Group and Carl Guardino,” said Yellow Cab General Manager Larry Silva. “So you’d have to assume that’s where the pressure came from.”

Liccardo said he changed his mind on fingerprinting all drivers after police leaders assured him the new system wouldn’t compromise safety.

“I was clear that I would not budge if the police felt that moving to an auditing system would backtrack on safety,” Liccardo said.

Guardino said he spent “less than a quarter hour” speaking with Liccardo about the issue. He said city leaders realized the ride-sharing pilot program wasn’t working and needed a “version 2.0.”

“What they tried in June wasn’t going to attract any participants,” Guardino said. “There was no pressure from our group and I’ll gently push back against any such insinuation.”

The taxicab companies aren’t happy with the compromises heading to the council Tuesday, and many airport cabdrivers plan to go on strike Monday. Silva said he’s surprised by the mayor’s “change of heart” and said auditing only 1 percent of ride-share drivers isn’t good enough. He argued that all taxicab drivers submit fingerprints and ride-share companies should follow the same rules.

“We would never give up fingerprints because we think it ensures safety of the public riding in taxicabs,” Silva said.

The proposal Tuesday also eliminates another rule contested by Uber and Lyft — vehicle age and mileage restrictions that barred drivers with cars older than 10 years or more than 400,000 miles. The city instead will rely on vehicle inspections performed by police for taxis and the CPUC for ride-share companies.

Silva said Yellow Cab won’t agree to that compromise, even with the city’s blessing, because of passenger safety concerns.

One mandate that remains in the city’s program is requiring ride-share drivers to obtain San Jose business licenses. Lyft officials protested the rule in the past.

Contact Ramona Giwargis at 408-920-5705, or follow her at Twitter.com/ramonagiwargis or.