The Military Readiness Enhancement Act would allow gays to serve openly in the military.
Wednesday, the committee members heard public comment before their decision.
"I understand what Mr. Clinton was trying to do with some dignity, but I think it's important for us to take the next step, and I think it's important for this council to support the legislation," said City Councilman Tony Young
The endorsement now moves to the full City Council for consideration.
Similar resolutions have passed in Los Angeles, San Francisco and Palm Springs.
San Diegans are going online to raise money to help make ends meet amid a partial government shutdown prolonged by a impasse over President Trump's demand for a wall along the U.S.-Mexico border.
Waterfront Park in downtown San Diego played host to thousands of people demonstrating in the third annual Women's March, which also took place in dozens of other cities across the country.
Three people robbed a San Carlos jewelry store on Saturday afternoon, then fled before officers were able to arrive, police said.
A record number of County employees will be hitting the streets next week to help count homeless people in the region.
People choosing not to vaccinate are now a "global health threat," according to the World Health Organization.