"We have sent a diplomatic note to the Venezuelan embassy today, saying that the request lacked sufficient basis from a legal point of view," a US official told reporters on condition of anonymity.
Venezuelan Ambassador Bernardo Alvarez submitted an extradition request to the US State Department on 13 May.
On Thursday, the top State Department official for Latin America, Roger Noriega, said he had not received a formal request from Caracas.
Posada Carriles, 77, has been under arrest in the United States since 17 May on immigration charges after requesting US political asylum.
Venezuela has demanded the extradition of Posada Carriles to stand trial for the downing of a Cuban airliner with 73 passengers aboard in 1976.
Born in Cuba, he became a citizen of Venezuela and was at the time of the bombing a member of Venezuela's intelligence service. Facing charges of involvement, he fled prison while awaiting an appeal of his trial.
"We have sent a diplomatic note to the Venezuelan embassy today, saying that the request lacked sufficient basis from a legal point of view"
US official on Carriles extradition request
Posada Carriles is also wanted in Cuba for the bombings of two Havana tourist hotels in 2000, in which an Italian businessman died.
He was found guilty in Panama of attempting to assassinate Castro at a summit in Panama City. The president of Panama at the time, Mireya Moscoso, pardoned him in 2004.
Posada Carriles was also a paid CIA operative for years after the Cuban revolution in 1959.
Venezuela, meanwhile, said on Friday that US officials had rejected only its request to arrest Posada Carriles, but not the request to extradite.
The embassy in Washington released a statement saying it would "submit any documentation necessary to seek the extradition."
The unnamed US official said, "so far we have not received a formal or acceptable request from any government".
Incoming Organisation of American States (OAS) Secretary General Jose Miguel Insulza said at OAS headquarters, "If officials of any country are serious about an extradition, they must treat it seriously and submit a request conforming to universal standards."
Castro and Venezuela's Hugo
Chavez share similiar political views
US officials have also said that they did not want Posada Carriles to be extradited to Cuba, nor extradited to a country that might then send him to Cuba.
The dustup came at as US-Venezuelan relations were at a low point, in part, because of Cuban President Fidel Castro's close relationship with Venezuelan President Hugo Chavez.