HONOLULU (AP) _ The Western Governors' Association is postponing its annual meeting that was to start June 16 in Honolulu because of ''apprehension over air transportation,''

The association's office in Denver said that although the governors' airline reservations ''had been taken care of sometime ago'' there was trouble getting participants to Hawaii because of the United Airlines strike.

Pilots began a strike nearly three weeks ago against United, which is the main carrier between Hawaii and the U.S. mainland.

Hawaii Gov. George R. Ariyoshi, association chairman, made the decision Tuesday afternoon, said a spokeswoman for the group in Denver.

The association said there is a possibility the conference will be rescheduled at a location to be determined. The spokeswoman, Tony Vigil, said in a telephone interview, she didn't know whether it would be in Hawaii or in another state.

Meanwhile, Ariyoshi's press secretary, Bob Wernet, said, ''The state of Hawaii continues to encourage people to travel to Hawaii.''

He said tourists have more flexibility in arranging travel schedules.

The Hawaii Visitors Bureau last week sent thousands of telegrams to U.S. travel agents encouraging travel to Hawaii.