SAN FRANCISCO  In one of the nation’s largest displays of support for gay rights, tens of thousands of people in cities across the country turned out in support of same-sex marriage on Saturday, lending their voices to an issue that many gay men and lesbians consider a critical step to full equality.

The demonstrations  from a sun-splashed throng in San Francisco to a chilly crowd in Minneapolis  came 11 days after California voters narrowly passed a ballot measure, Proposition 8, that outlawed previously legal same-sex ceremonies in the state. The measure’s passage has spurred protests in California and across the country, including at several Mormon temples, a reflection of that church’s ardent backing of the proposition.

On Saturday, speakers painted the fight over Proposition 8 as another test of a movement that began with the riots at the Stonewall Inn in New York in 1969, survived the emergence of the AIDS crisis in the 1980s, and has since made enormous strides in societal acceptance, whether in television shows or in antidiscrimination laws.

“It’s not ‘Yes we can,’ ” said Tom Ammiano, a San Francisco city supervisor, referring to President-elect Barack Obama’s campaign mantra. “It’s ‘Yes we will.’ ”