More than 40,000 employees at AT&T Inc will keep working under the terms of an expired labor contract while their union continues negotiations with the telephone company, averting a potentially costly strike for now.

The workers in AT&T's traditional wireline telephone business and some other units voted recently to give their union, the Communications Workers of America, authority to call a strike ahead of the expiration of four separate labor contracts at midnight local time April 7.

AT&T, whose total workforce is roughly 256,000, is looking to trim worker benefits to cut costs in its wireline business, which has declined rapidly in recent years. But the union says AT&T is seeking too many concessions. In particular, it says that AT&T wants to significantly increase healthcare costs for workers.

At midnight eastern time April 7, contracts expired for almost 10,000 workers, including almost 6,000 so-called legacy AT&T workers in various states and about 4,000 workers in the eastern United States.

The union said just after midnight eastern time on Saturday that it made some progress but had a lot of ground yet to cover to reach agreement with the company. At midnight central time, a contract covering thousands more AT&T workers in the midwest region expired. AT&T said that the midwest contract covers 13,000 people while the union said it covers 15,000.

At midnight Pacific time, a fourth contract that the union said covered about 18,000 workers in western states such as California and Nevada also expired. Negotiations were continuing in that region as well, according to a union statement.

AT&T said the negotiations reflected the spirit of the longstanding relationship between AT&T and the union.

Last August, AT&T's rival, Verizon Communications, had to cope with a two-week strike after contracts expired for 45,000 workers. Roughly eight months later, Verizon is still negotiating with unions for a new contract.

AT&T has been negotiating with the CWA on the four contracts since February. Contracts covering another 30,000 AT&T wireline workers expire in coming months, the company said.

The last time AT&T faced a big strike was in 2004 when 100,000 workers walked out for four days on the company, which was then known as SBC Communications. SBC changed its name to AT&T Inc after it bought AT&T Corp in 2005.

(Reporting By Sinead Carew; Editing by Ron Popeski)