Ms Chesimard, now 50 and calling herself Assata Shakur, is one of nearly 100 serious criminals who fled the United States and were granted political asylum by Mr Castro's communist regime. The Clinton administration has asked Cuba to hand them over but Mr Castro refuses.
New Jersey governor Christine Todd Whitman on Thursday offered a $100,000 (pounds 60,000) reward to anyone who brings Ms Chesimard back to complete a life sentence handed down in 1977. She broke out of jail in a daring escape in 1979, when her visitors, former comrades in a militant black group, took a guard hostage.
She is believed to have fled to Cuba in 1984, where she has since become a grandmother and taken a master's degree. She says she did not shoot New Jersey State Trooper Werner Foerster on 2 May 1973.
Joining in the campaign to return her and the other American criminals harboured by the Cuban government, New Jersey Republican Congressman Bob Franks described Ms Chesimard as "a cold-blooded cop killer" and said Washington should not consider improving relations with Havana until all the American convicts are returned.
"This is normal behaviour for Fidel Castro, to give safe haven to terrorists, to drug dealers, to cop killers," said Republican Florida Congresswoman Ileana Ros-Lehtinen, a Cuban-American. In its annual report on international terrorism, published yesterday, the US State Department listed Cuba among countries harbouring terrorists.
Responding to the calls to return Ms Chesimard, a Cuban government spokesman noted that Havana has no extradition treaty with Washington and did not necessarily believe Ms Chesimard was guilty.
Among the other American convicts in Cuba is former Black Panther William Lee Brent, now 68, who hijacked an American domestic airliner to Cuba in 1969. Cuba first jailed Mr Brent for almost two years, suspecting he may be a CIA agent, but then freed him. He works as a disc jockey and announcer on Cuban state radio.