Nassau County Executive Edward Mangano and Oyster Bay Town Supervisor John Venditto were arrested Thursday and charged with receiving “bribes and kickbacks” from a businessman who also gave Mangano’s wife a lucrative no-show job, federal authorities said.

The federal corruption charges center on a relationship involving Mangano, Venditto and a person identified only as a co-conspirator in the 13-count indictment, but whom sources identified as Long Island restaurateur Harendra Singh.

Republicans Mangano, 54, of Bethpage, and Venditto, 67, of North Massapequa, are charged with conspiracy to commit bribery, fraud and obstruction of justice. Mangano is also charged with extortion, and Venditto with making false statements to federal agents.

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“Sadly, we’re getting confronted with public officials who are alleged to have abused their positions of trust, in this case the highest-ranking elected official in Nassau County and in the Town of Oyster Bay, for their own corrupt benefit, thereby abusing the public trust,” Robert L. Capers, U.S. attorney for the Eastern District of New York, said at a news conference.

“Mr. Mangano and Mr. Venditto received bribes and kickbacks from their co-conspirator on an on-demand basis or as opportunities arose in connection with business dealings in Nassau County or the Town of Oyster Bay,” Capers said.

Mangano’s wife, Linda, is charged with obstruction and making false statements. Capers said she received more than $450,000 from the no-show job from April 2010, months after her husband took office, to August 2014.

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One of her phony jobs was to serve as a “food taster,” he said.

Authorities accuse Edward Mangano and Venditto of scheming to award Singh contracts worth hundreds of thousands of dollars to provide food services to county agencies and secure multimillion-dollar loan guarantees for his businesses.

In exchange, Mangano and Venditto received gifts from the co-conspirator, including “hotel and travel expenses, limousine services, free meals and other gifts,” according to the indictment.

Among the gifts Mangano received were a massage chair worth $3,600, an ergonomic office chair worth $3,300, a Panerai Luminor watch worth $7,300 and installation of hardwood flooring in his bedroom, authorities said.

In return for helping the businessesman, Venditto got use of a private room at a restaurant, free chauffeur service for himself and his family, and discounted fundraisers at a restaurant, according to the indictment.

The restaurants are not identified in the indictment, but sources said the fundraisers were at Woodlands at the Town of Oyster Bay golf course, previously operated by Singh, and the private room was at Singh’s flagship restaurant in Bethpage, H.R. Singletons.

News of the arrests spurred some Republican politicians to immediately call for Venditto and Mangano to resign.

If convicted of the top count, they face up to 20 years in prison. The charges resulted from an investigation by federal prosecutors, and FBI and IRS agents.

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At their arraignments at federal court in Central Islip, all three pleaded not guilty through their attorneys and were each released on $500,000 bond.

Linda Mangano, 54, wept during the brief arraignment before U.S. District Judge Sandra Feuerstein in Central Islip.

Capers said Edward Mangano was charged with extortion for demanding that Singh provide the no-show job for his wife.

The Manganos and Venditto are also accused of obstructing justice in an attempt to cover up the alleged scheme, Capers said. Linda Mangano and Venditto lied to federal agents who questioned them, according to the indictment.

In return for the money and favors from Singh, official actions taken by Mangano and Venditto included helping Singh get the Town of Oyster Bay’s guarantee on four loans totaling more than $20 million, authorities said.

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According to the indictment, Mangano “pressured” Venditto to amend Oyster Bay contracts to benefit the co-conspirator. The businessman also got two lucrative contracts worth hundreds of thousands of dollars to provide food services to various county agencies.

One contract involved the supply of $200,000 worth of bread and rolls to the Nassau County jail in June 2012; the second was for providing $237,000 worth of food to county workers in the aftermath of superstorm Sandy, the indictment said.

After the arraignment, Mangano said he had no plans to step down and promised evidence “that rebuts any of this nonsense — that I would ever do anything that sacrifices this oath of office.”

He said the case involves a friend of the family for 25 years but did not elaborate. Singh is a longtime friend of Mangano.

“It’s ridiculous, but I can’t say any more,” Mangano said. “I’m going to continue to govern. I’m going to go to work. America’s the greatest country in the world. And you’ll have an opportunity to hear everything and decide for yourselves. God bless you.”

Mangano’s lawyer, Kevin Keating of Garden City, refuted the allegations that the county executive was involved in a scheme to get Singh county contracts.

“The indictment is utterly devoid of any coherent allegation that Mr. Mangano engaged in any official action for Mr. Singh — as he did not,” Keating said in a statement. “These charges will be vigorously defended as Mr. Mangano continues to serve the County.”

The attorney also disputed the allegations involving Oyster Bay, saying Mangano “had absolutely no authority or influence over any decision Oyster Bay officials made to extend to Mr. Singh a loan guarantee.”

There is no record of Singh getting paid for providing bread to the jail, and sources said he withdrew from fulfilling the contract. But it would be a crime to obtain the contract in a corrupt manner even if it wasn’t fulfilled.

Keating declined to respond to a question about the jail contract.

Linda Mangano’s attorney, John Carman of Garden City, declined to comment afterward.

Venditto did not comment Thursday, but his attorney, Brian Griffin of Garden City, said in a statement: “John Venditto has served the citizens of the Town of Oyster Bay for 40 years, with great distinction. He has been diligent, caring and ethical throughout his years of service.

“Although Mr. Venditto takes this indictment seriously, to be very clear, he has entered a not guilty plea and intends to defend against it vigorously,” Griffin said.

Griffin declined to say whether Venditto plans to continue in office.

Assistant U.S. Attorney Lara Treinis Gatz said during the arraignment that the government wants to have Griffin removed as Venditto’s attorney because the federal investigation is continuing into Nassau County and the Town of Oyster Bay, and Griffin has a conflict of interest.

Gatz, who is conducting the overall corruption investigation along with prosecutors Catherine Mirabile and Raymond Tierney, said Griffin represents other people involved in the investigation.

Gatz did not name the others, but Griffin also represents Mangano’s chief deputy, Rob Walker, who has acknowledged that he is part of an ongoing investigation into Nassau contracts. Walker has not been charged with any crimes and has denied any wrongdoing.

Griffin said he had explained the situation to Venditto, who had no objection to Griffin continuing to represent him.

Feuerstein gave the government until Oct. 28 to submit motions as to why Griffin should be removed.

Anthony La Pinta, the attorney for Singh, who has been reported by Newsday to be in plea negotiations with prosecutors, declined to comment on the status of Singh’s cooperation with the government, if any.

In a statement released after the hearing, La Pinta said: “My priority is to provide Harendra Singh with the most powerful legal defense possible and to continue to fight for him, regardless of who else is charged in this investigation. I remain committed to protecting Mr. Singh’s rights and ensuring that his case proceeds in a fair and favorable manner.”

According to sources familiar with the government’s case, it did not depend on Singh’s cooperation.

In Long Island’s Eastern District, Singh faces more than 10 years in prison if convicted on a September 2015 indictment charging him with fraud and with bribing a former Oyster Bay Town employee.

On Wednesday, sources said Singh is negotiating with federal prosecutors to avoid future indictments and get a lesser sentence.

With Ted Phillips and Paul LaRocco