ALBANY – In the four-way race for a state Senate seat in the Bronx, many of the most influential labor unions are lining up behind the preferred candidate of the Senate’s Republican leadership, Assemblyman Stephen Kaufman.

Today, Mr. Kaufman will formally accept the endorsement of SEIU Local 1199, representing 250,000 health-care workers across the state. He previously received the support of the AFL-CIO of New York State, New York State United Teachers, the unions representing New York City police, firefighters, and sanitation workers, and others.

These endorsements from unions – which are in a position to support candidates with cash, volunteers, and phone banks – give Mr. Kaufman an edge in what is expected to be a hard-fought race to replace Senator Guy Velella, who pleaded guilty earlier this year to bribery-related charges.

A Democrat first elected to the Assembly in 1988, Mr. Kaufman is running in three party primaries on September 14 – for the Democratic, Republican, and Conservative nominations. He is backed by the Senate majority leader, Joseph Bruno, and is widely expected to join the Republican conference if elected.

“Stephen Kaufman has been an advocate for quality healthcare throughout his tenure in the state Assembly, and we’re proud to stand next to him for his Senate bid,” the president of Local 1199,Dennis Rivera, said in a statement.

Mr. Kaufman’s rivals argue that 1199 and the other unions are acting under pressure from Mr. Bruno, who is eager to preserve his 37-24 GOP majority in a predominantly Democratic state.

“It’s because Joe Bruno…has been holding the ax over unions’ heads to endorse Kaufman or they won’t get legislation through,” said the other candidate for the Republican and Conservative nominations, John Fleming.

“[Bruno’s] got all these traditional liberal unions working on behalf of a Republican,” said a spokesman for Assemblyman Jeffrey Klein, Jordan Isenstadt. “It’s certainly unfortunate, and we’re certainly disappointed.”

Mr. Klein competing in the Democratic primary against Mr. Kaurman and Egidio Sementilli, a Bronx community board member.

A spokesman for Mr. Kaufman, John Gallagher, insisted the endorsements are a reward for “supporting working men and women throughout his career in public office.”

“These endorsements are based on Steve’s record, not speculation about the future,” Mr. Gallagher said.

A top official at Local 1199, Jennifer Cunningham, acknowledged Mr. Kaufman’s alliance with the Senate Republicans was a factor in the endorsement.

“There are benefits to being in the majority,” Ms. Cunningham said. “To the extent your voice is just a little bit louder in the majority, and you’re an advocate of quality health care, then 1199 would like to be supportive.”

A spokesman for Mr. Bruno, John McArdle, said the charges of arm-twisting are “nonsense.”

Union officials, “like a lot of people, see that he is the best candidate to fill that Senate seat,” Mr. McArdle said.

Mr. Fleming – the former coordinator of Mayor Giuliani’s security detail – criticized Mr. Kaufman for accepting the 1199 endorsement. He argued that legislators who support the union’s agenda are driving up the cost of Medicaid, the government health plan for the poor and disabled.

“He’s placating 1199 at the expense of taxpayers,” Mr. Fleming said of Mr. Kaufman.

Mr. Klein has won the support of some unions, including locals of the Communications Workers of American and the United Food and Commercial Workers, along with interest groups such as the New York League of Conservation Voters and the anti-poverty group ACORN.

He also received an endorsement yesterday from Senator Schumer, who, like most sitting senators, generally avoids taking sides in Democratic primaries.

“It is important that we get Jeff Klein elected so that Democrats can finally take back the state Senate,” Mr. Schumer said in a statement.

Also backing Mr. Klein are prominent Democrats such as the attorney general, Eliot Spitzer; the state comptroller, Alan Hevesi, and the president of the Bronx, Adolfo Carrion.

Mr. Kaufman, meanwhile, has the support of Bronx Democrats such as Assemblyman Jeffrey Dinowitz and Council Member Madeline Provenzano of the Bronx, along with Republicans such as Governor Pataki and Mayor Bloomberg.

Mr. Fleming said he will be announcing several endorsements by politicians and community organizations over the next two weeks. Mr. Fleming’s former boss, Mr. Giuliani, considers him a “dear friend” and supported him in a previous race for Congress, but is staying neutral in the Senate race until after the Republican primary, according to his spokeswoman, Sunny Mindel.