AC Transit’s board of directors is asking Gov. Jerry Brown to seek a 60-day cooling-off period to eliminate the possibility that the bus agency’s employees will go on strike this week.

The board’s request comes a day after Amalgamated Transit Union Local 192, which represents about 1,800 bus drivers, mechanics, dispatchers, clerical staff and other workers, issued a 72-hour strike notice and threatened a walkout starting at 12:01 a.m. Thursday.

AC Transit, which logs about 200,000 daily bus rides by passengers in Alameda and Contra Costa counties, has twice reached tentative agreements with union leaders on a new contract, but union members have rejected both agreements.

Employees voted 561 to 369 against a tentative agreement Oct. 1, and voted down a previous tentative pact Aug. 17 by a margin of 576 to 257.

AC Transit management says it is offering employees a 9.5 percent pay increase over three years, which would give them an average of an additional $5,529 in annual income even after medical contributions are factored in.

In their letter to Brown, AC Transit board members said they are asking for a cooling-off period because a strike would leave riders stranded and “significantly endanger the public’s health, safety and welfare.”