The US has rejected Venezuela's request for it to arrest a Cuban-born man, Luis Posada Carriles, over a 1976 airline bombing that killed 73 people.
The row has strained relations between Venezuela and the US
Washington told Caracas, which wants to see him extradited, that there was not enough evidence to back the request.
The 77-year-old was charged last week with illegal entry into the US.
The former CIA employee has denied involvement in the plot to blow up the Cubana Airlines plane on a flight from Caracas to Havana.
Venezuela could make a full extradition request if it provides more evidence, a US state department official told reporters.
Mr Posada Carriles faces a hearing at a US immigration court on 13 June, which could decide to deport him.
He is expected to apply for asylum at that hearing.
A naturalised Venezuelan, Mr Posada Carriles was twice acquitted by Venezuelan courts of plotting to bomb the plane.
He escaped from a Venezuelan prison in 1985 while awaiting a trial on appeal.
Luis Posada Carriles denies involvement in the airliner bombing
The US says it will not deport Mr Posada Carriles to any country that would hand him over to Fidel Castro's regime in Cuba.
Venezuela has said it will not hand Mr Posada Carriles over, and Mr Castro has insisted he will be happy to see him tried there.
Earlier this week, Venezuelan President Hugo Chavez said he would consider breaking diplomatic ties with the US if the extradition request was knocked back.
But on Friday, a statement from Venezuela's foreign ministry said Mr Chavez's comments "cannot be considered an ultimatum".
It said Caracas would push for Mr Posada Carriles to be handed over.