PHOENIX — Negotiators for striking transit bus drivers in eastern Phoenix suburbs and the national bus company they work for negotiated Friday, the second day of a work stoppage affecting tens of thousands of riders.

The strike began Thursday, shutting down 40 routes in Chandler, Gilbert, Mesa and Tempe, along with express routes from those cities to Scottsdale and Phoenix. The affected routes serve some 57,000 riders daily, including many workers without cars who can't walk miles to work in the summertime heat.

Negotiators for the Amalgamated Transit Union Local 1433 and operator First Transit met for a few hours Thursday and held talks again on Friday. First Transit took over operations July 1 after winning a three-year contract from the Valley Metropolitan Regional Transit Authority with options for seven additional years in January. The region's single light rail line from north-central Phoenix to Mesa was operating normally, as was bus service in Phoenix and western suburbs.

Transit authority spokeswoman Susan Tierney said the agency is not involved in the negotiations. The new contract combined operations in Mesa and Tempe that serve the eastern Phoenix suburbs, and involved savings of $36 million over the previous contract by operating both parts of the system together and streamlining operations. Union officials said it cut $77 million over 10 years.

ATU Local 1433 president Bob Bean said Friday afternoon that there's optimism an agreement will be reached. First Transit spokeswoman Jen Biddinger also said the sides are making progress.

Maurice L. Harris, another First Transit spokesman, said later that talks concluded for the day at about 6:30 p.m., after the union called for a one-year contract.

Harris said in the press statement that all discussions up to that point had hinged on a three-year contract, which he maintained would provide for greater bus service stability for riders.

Union spokesmen did not immediately return calls for comment.

Earlier, union officials said the company provided a new offer on a key issue, job security. Drivers on the picket line in front of Tempe bus yard Thursday said that was their biggest issue with First Transit.

The contract between the regional transit authority and First Transit would override First Transit's proposed deal with the union, because of a clause within the labor contract, union members said Thursday.

"It doesn't protect our members, it doesn't protect any of the operators," said James Washington, a driver for 23 years who serves on the board of Amalgamated Transit Union's Local 1433. "It gives management the right to run rampant and do whatever they like and their client basically dictates what they need to do to us."

It wasn't immediately known if the new offer on so-called "management rights" had been accepted by the union. First Transit also said it has offered higher wages and lower health care costs.

A striker said Friday that union members were united and would remain on the picket lines "as long as it takes."

"The strike is going well," driver Shirley Henderson-Manley said. "It's going in our favor so far."

A strike in March 2012 crippled bus service in metropolitan Phoenix for six days before it was settled.