Mayor Bloomberg is preparing for a rematch with Albany lawmakers over a plan to construct a 35-story building for the United Nations on a playground next to its Turtle Bay site.

The state Legislature in 2004 refused to consider the plan after a number of senators blasted the institution as anti-American and attacked it for the oil-for-food scandal.

Sources said Mr. Bloomberg, who has been in favor of the construction from the start, is quietly reviving his lobbying effort for the project, which needs state approvals. They said he would make it a front-and-center issue once the state budget is finalized.

Mr. Bloomberg’s chief spokesman, Stuart Loeser, declined to comment on specifics, but said the project is “something we’ve worked on and something we will continue to work on.”

He added: “There was a bill introduced in 2004, and we believe that the bill should be reintroduced. We have pushed to keep the U.N. in New York City in the past and nothing has changed.”

Other Bloomberg sources said the renewed push, first reported by the New York Post, may be modified somewhat but would again rely on the mayor’s rationale that the United Nations is a crucial economic engine for the city. They said the construction unions, whose members would likely be first in line for jobs during the building of the 35-story tower at Robert Moses Park, would be on board with the effort.

“The U.N. is a major economic engine for the city of New York,” Mr. Loeser said. “It generates $2.2 billion in economic activity every year and accounts for more than 18,000 jobs.”

Council Member Simcha Felder, a Democrat who represents the Boro Park section of Brooklyn, said yesterday that he doesn’t know what the mayor’s plans are, but that he is just as adamantly opposed to the expansion as when it was first proposed.

“The United Nations is den of wolves,” he said. “It is true that the economy of the city is critical and we must take extraordinary steps to keep it going, but there comes a point where one must say: Are we sacrificing any moral beliefs?”

Mr. Felder, who enthusiastically backed Mr. Bloomberg for re-election last year, said he would “respectfully disagree” with the mayor if he did go to bat for the United Nations.

“They hate America, they hate the United States, and they hate all of our allies. What are we doing helping a body that hates us?” he said. “The mayor is the best mayor this city has ever had, but he is not God and he makes mistakes as do I,” the council member said.

Rep. Anthony Weiner, who has criticized the United Nations as virulently anti-Israel, reiterated yesterday his past position that the city should use the proposed development project to demand reforms from the international body.

Mr. Weiner, who ran in the Democratic mayoral primary last year, said there is “no doubt that the U.N. is a large and important employer in New York,” but he said this is the city’s “moment in time” to push for changes.

“The mayor should always use the bully pulpit of his position,” he said. “The U.N. probably won’t listen any other time but now.”

In 2004, the state Senate declined to consider a bill on the U.N. expansion. At the time, the Senate’s Republican majority leader, Joseph Bruno, cited a lack of financial accountability and “tremendous community opposition” to the expansion. As part of that proposal, the U.N. Development Corporation, a city-state public benefit corporation, was expected to put up $600 million in bonds to finance the project. That money would be collected from the body’s member nations, but there would be no state oversight.

A spokesman for Mr. Bruno, Mark Hansen, yesterday said the senator is focused on the state budget and that “nothing has changed” with the U.N. expansion project.

When asked whether Mr. Bruno would rule out reviewing new legislation, he said: “I’m sure it will be reviewed with many other issues, but right now we are focused on the budget.”

Bloomberg officials said that proposal could be modified when it is revisited, but none of those details have been hashed out. It was unclear yesterday whether they had a sponsor on board in the Senate.

Meanwhile, the assistant secretary, general of the Capital Master Plan, Fritz Reuter, said yesterday the renovation of the dilapidated 54-year-old United Nations building had moved forward. He said the organization has “solved our problems on-site.”

The United Nations is planning to erect a temporary building on the northern parcel of its property and do the renovation in phases. That building, Mr. Reuter said, could be in use by early 2007.The renovations, which he said are estimated to cost nearly $1.6 billion, are scheduled for completion by 2014.

U.N. officials would likely be pleased to have the new space so they could consolidate employees, which are now scattered in office buildings around the city.

A new building also could mean the emptying of two other U.N. buildings that are owned by the city. If employees working in those buildings are consolidated in a new tower, the city could sell those buildings for a profit.