LOS ANGELES — Hollywood writers said they would strike for the first time in nearly 20 years but left open the door for last-minute talks to avert a crippling walkout.

The president of the Writers Guild of America, Patric Verrone, drew loud cheers when he announced in closed-door session last night that the union could strike as early as Sunday, several writers said.

However, guild officials said privately the strike would most likely start on Monday.

The WGA board was to meet this morning to approve the strike and set a time for the first picket lines. A strike captains’ meeting was set for tomorrow morning.

Union leaders said they would delay the action if producers showed movement in contract negotiations — especially on the key issue of paying writers when TV episodes are sold or streamed over the Internet.

“It’s going to have to be a good deal, but we would much rather negotiate than go on strike,” a WGA chief negotiator, John Bowman, said.

The president of the Alliance of Motion Picture and Television Producers, Nick Counter, said in a statement the alliance was not surprised by the strike announcement.

“We are ready to meet and are prepared to close this contract this weekend,” he said.

The first casualty of the strike will likely be late-night talk shows, which are dependent on current events to fuel monologues and other entertainment.

The strike will not immediately impact film or prime-time TV production. Most studios have stockpiled dozens of movie scripts, and TV shows have enough scripts or completed shows in hand to last until early next year.

About 3,000 of the union’s 12,000 members attended yesterday’s meeting. Writers said the line of questioning inside the meeting wasn’t whether the group was going to strike, but how the job action would be carried out.

“Where the membership stands could not be more clear,” an executive producer of the television drama “Lost” and a member of the guild negotiating committee, Carlton Cuse, said. “There was not a single dissenting voice in the room.”

Guild members already had authorized their negotiators to call the first strike since 1988. That strike lasted 22 weeks and cost the industry about $500 million.

The mood was more subdued as writers filed out of the building and headed to their cars.

A veteran TV writer, Janis Hirsch, was among the 10% who had voted against striking.

“It’s sad, but I’ve got to support my union. At this point it makes sense,” she said.

The stakes are high for writers, actors, and directors. While the revenue generated by Internet sales and rentals of films and TV shows is minuscule compared to DVDs, the guilds say Internet revenue eventually will become dominant.