The Alexandria City Council indicated yesterday it will no longer oppose introduction of a 911 emergency telephone system in Northern Virginia if the region's other jurisdictions agree to move toward a more costly, computer-assisted 911 system in the future.

If the suburban communities agree to do that, it would quell a controversy that began last spring when the Alexandria council killed a 911 proposal area planners have been debating since 1971. Both Maryland suburbs and the District of Columbia have had 911 service for years.

The Alexandria council agreed yesterday to vote on the issue Nov. 25 and several members of the council indicated during a discussion they are ready to back the system. Their change of stance came after John F. Herrity, chairman of the Fairfax County Board of Supervisors, made an unusual appearance before the council and offered a compromise settlement.

Under it, all other Northern Virginia governments would formally state their intention to convert to the more complex "Enhanced-911" system, which Alexandria wants, when it becomes available in 1982. In return, Alexandria would remove its opposition to the currently available "Basic-911" system, which the other jurisdictions want immediately.

"That's a good suggestion," Alexandria Mayor Charles E. Beatley Jr. told Herrity yesterday. "I can tell it came from the heart."

Herrity said that there are 13 different emergency telephone numbers Northern Virginia residents must sort through when seeking emergency help. Moreover, many Northern Virginians don't know which jurisdiction would provide them with emergency service, he said.

"I've lived in the area all my life, and when I had a heart attack four years ago it took us a few minutes to figure out which emergency service unit to call," Herrity said.

Herrity said the Fairfax board would back his proposal. The Arlington County Board has opposed the enhanced 911 system because of its cost. Spokesmen for Arlington were noncommittal and the other local governments involved could not be reached for comment. Both Herrity and Beatley expressed optimism that the new agreement would be approved by all Northern Virginia localities.