Even with tens of thousands in northwest Queens having no electricity as of yesterday — about a third of the total affected by a week-long blackout — Mayor Bloomberg and Con Edison officials are saying they cannot give a concrete time when power will be fully restored.

Earlier, Mr.Bloomberg gave an assurance that the utility company would likely be able to restore everyone’s power by yesterday.

The chairman of Con Ed, Kevin Burke, amid calls for his resignation, said power is being restored to thousands of customers every day. However, a revised weekend announcement that swelled the estimated number of affected New Yorkers by tenfold reverberated yesterday, with furious local elected officials demanding the governor officially designate the darkened communities disaster zones.

“Why is our governor incapable of speaking a week now into this tragedy?” an assemblyman who represents the area, Michael Gianaris, said shortly after appearing at a press conference during which Mayor Bloomberg dismissed calls for state involvement.

“Not a word from George Pataki, not a peep, not his face on TV, not his voice on the radio, nothing,” he said.

An hour earlier, Mayor Bloomberg said he’s spoken to the governor several times about the crisis, which has affected parts of Astoria, Hunters Point, Long Island City, Sunnyside, and Woodside.

Disaster-area requests need to be made first by the affected municipality, a spokesman for the governor’s office in Albany, Saleem Cheeks, said. Mr. Bloomberg indicated that he didn’t want the emergency designation.

Separately, a City Council member who represents the area, Eric Gioia, called for Con Ed’s chief to resign, repeating a popular allegation in northwest Queens that Mr. Burke had lied to the public about the breadth of the outages. Earlier, Mr. Gioia — who has also asked the Queens district attorney to conduct a criminal investigation into Con Ed — stood nearby as the mayor praised the utility’s response to the crisis.

Late yesterday, Mr. Burke deflected calls for his resignation and said Con Ed had been forthright.

“I think that what we’ve been communicating to people is the best information that we have,” Mr. Burke, who started with the company in 1973, said. “And we’re going to continue to do that.”

Mr. Bloomberg said Thursday that he expected power to be restored to most of the blacked-out areas by last Friday for some and yesterday for most. But weekend storms and a gross underestimate of the number of those affected led officials to revise that timetable.

The blackouts began to cascade through northwest Queens early last week when 10 of the nearly two dozen feeder cables in the ground that transmit electricity to northwest Queens melted from the extreme heat, forcing the remaining intact cables to shoulder all the demand.

Con Ed and city officials initially said hundreds of customers had lost power. The term “customer” can be misleading, though, because a “customer” can be a single person’s house or an entire apartment building. By one rough though commonly used metric, each “customer” represents about three people. Late yesterday, a Con Ed spokesman said the power to about 19,000 customers had been restored, with 6,000 to go.

All of the damaged cables have been repaired, Mr. Burke said, and Con Ed is working with guest crews from other utility companies who have come to help the city from across the Eastern Seaboard.

The comity among electrical companies seemed to provide little comfort to the thousands of people and businesses who have spent the past week without regular electricity. A cashier at Smiley’s Fruits and Vegetables in Sunnyside, Hwan Kang Oh, said over the hum of a street-side power generator that his store has had to throw out pounds of milk, produce, and ice cream. The generator costs more than $3,000 a week, Mr. Oh said. Con Ed has promised to reimburse merchants for such losses.

Through a translator, Mr. Oh questioned whether more affluent parts of New York City would be allowed to stew without power for a week.

For his part, Mr. Bloomberg has defended Con Ed’s response to the crisis in the face of mounting criticism from the Queens political delegation.

“In summary, I guess, Con Edison is making progress,” the mayor said yesterday morning. “Are we satisfied with the progress? It is what it is.”

That assessment infuriated more than a half dozen local Astoria park-goers and dog-walkers who glared at Mr. Bloomberg’s morning news conference held just behind police cordons. There was a brief confrontation reminiscent of a mayoral visit to Queens in 1969 to assess the snow that the city had let pile up. Back then, angry residents hurled invective at New York’s 103rd mayor, John Lindsay.

“Do something,” someone shouted this time, at Gotham’s 108th mayor as he stood by his motorcade near powerless Astoria. “You’re a bum.”