SAN JOSE — Dozens of airline passengers were left at the curb in a downpour Monday after 300 airport taxicab drivers motored off the job in a strike over San Jose’s ride-booking policies that is poised to spread citywide.

Cab drivers circled past bewildered air travelers, honking their horns, and protested with signs outside City Hall. The cabbies plan to strike throughout San Jose on Tuesday to coincide with a meeting where the City Council will discuss eliminating strict regulations on ride-booking companies such as Uber and Lyft.

If the drivers don’t get what they want from the council, they may continue the strike Wednesday and possibly beyond, but only at the airport.

Steve Damran, 29, was among the many people who arrived at Mineta San Jose International Airport on Monday morning to find they couldn’t catch a cab. He stood in the taxi line at Terminal A after returning a car he’d rented for a weekend road trip to Anaheim.

The San Jose resident said he’s followed the conflict between cabbies and ride-booking companies.

“I can see why the drivers are upset, but competition is good,” said Damran, who added that “to strike on a rainy day is crazy.”

The city’s ride-booking rules, adopted in June, called for Uber and Lyft drivers to undergo fingerprints, meet vehicle age and condition requirements and obtain business licenses before operating at the airport — the same rules imposed on cab drivers.

But two months after the rules went into effect, both Uber and Lyft snubbed the airport — not a single driver signed up for the program. Now city officials are thinking about dumping those rules in favor of a compromise, triggering an outcry from the taxi industry.

“They want to change the rules in the middle of the game,” said Shakur Buni, president of the San Jose Airport Taxi Driver Association at the airport. “We are asking them for equal regulations.”

Barring a last-minute deal with the city, Buni said 700 cab drivers citywide could go on strike Tuesday — not just the 300 drivers at the airport. Buni, a Yellow Cab driver of more than 20 years, stood outside City Hall on Monday, cheering on drivers who were holding signs that said, “Uber is not above the law.”

Taxicab leaders emailed a list of demands to Mayor Sam Liccardo and the council, which included lowering taxi trip fees and maintaining the strict rules for ride-booking. The mayor’s office was planning to issue a response late Monday.

After driving a Green Cab for 25 years, Kindie Setegne said San Jose’s “unfair” regulations will drive him out of town.

“I’ve been getting sick from the stress,” said Setegne, 57. “We’re not against Uber and Lyft, but they need to go by the rules. We need fairness for both industries.”

The council Tuesday will mull over a watered-down version of the original rules for ride-booking: random audits of 1 percent of drivers instead of mandatory fingerprints for all and no more vehicle age and condition restrictions.

The monthly auditing process, a model used in San Diego, would include random curbside audits using mobile fingerprinting equipment. The audits would verify a ride-booking driver’s identity and review his criminal history.

Said Ali, 52, a Green Cab driver of 17 years, said that’s not good enough. All taxi drivers get fingerprinted, he argued, and the mobile app-based companies should do the same.

The strike caught some travelers by surprise and sparked frustration as they scrambled to find alternatives.

Roger Tiu and his wife, Carrie Bobier-Tiu, were temporarily stranded at the airport following an early flight home from Las Vegas. The Sunnyvale couple had planned to take taxis straight to work following a long weekend in Sin City.

Instead, they were in a line with about a half-dozen other travelers watching dozens of striking cabbies drive by while blasting their horns.

“We’re trying to figure out what we’re going to do,” Bobier-Tiu said.

Tiu said he is for allowing ride-booking companies to operate out of the airport but believes the city should treat both groups the same.

“I would prefer they make it less restrictive for cabbies than more restrictive,” Tiu said.

The taxicab strike continued late into the evening. Airport officials eased the pain of the work stoppage with some advance planning, said spokeswoman Rosemary Barnes. She said the airport’s door-to-door shuttles and limos “stepped up to the plate” to help travelers.

Liccardo was a staunch supporter of fingerprinting ride-booking operators but relented in a memo late Friday afternoon. Liccardo said he changed his mind after police officials told him the random audits wouldn’t compromise safety.

In abandoning its attempt to fingerprint Uber and Lyft drivers at the airport, San Jose will consider appealing to the California Public Utilities Commission, the agency that regulates ride-booking companies, to require fingerprinting of all drivers statewide. Los Angeles International Airport and San Francisco International Airport have made similar requests, city officials said.

And in an effort to “level the playing field” between cabbies and their high-tech competition, the City Council next week will discuss deregulating taxis.

Some ideas include a simpler vehicle inspection process, issuing temporary permits while waiting for background checks, and using the same random auditing system instead of fingerprinting all taxi drivers.

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