Venezuela has said the US will be guilty of double standards on terrorism if it does not extradite a Cuban exile wanted over the bombing of a plane.
Luis Posada Carriles poses a problem for the US government
Venezuelan President Hugo Chavez said the man, Luis Posada Carriles, was "a self-confessed terrorist".
He said the US had no choice but to send him back to Venezuela, where he escaped from jail two decades ago.
Venezuela wants the man to stand trial over the bombing of the Cuban plane in 1976 that killed 73 people.
Mr Posada Carriles - who was born in Cuba but now holds Venezuelan nationality - has denied involvement in the attack on the Cuban airline passenger plane on a flight from Caracas to Havana.
The 77-year-old former CIA collaborator was charged on Thursday with illegal entry into the US - weeks after he smuggled himself into the country.
Mr Posada Carriles will be held in custody until an immigration court hearing on 13 June, US immigration officials said.
His lawyer said he had been given the right to live permanently in the US more than 40 years ago.
'World is watching'
"We demand the US government stop its hypocrisy and its two-faced attitude and send this terrorist, this bandit to Venezuela," Mr Chavez told reporters.
"He is a self-confessed terrorist... The US has no choice, either send him to Venezuela or be seen by the world as protecting terrorism," he said.
"The world is watching," Mr Chavez added.
Mr Posada Carriles escaped a Venezuelan prison in 1985 while awaiting a trial on appeal.
He was twice acquitted by Venezuelan courts of plotting to bomb the plane.
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.
US Immigration and Customs Enforcement (ICE) on Thursday charged Mr Posada with "entering the United States without inspection in violation of the Immigration and Nationality Act".
The ICE statement said that Mr Posada Carriles would be able to contest his detention at the hearing before an immigration judge.