His remarks follow an offer from his brother, President Raul Castro, to meet Mr Obama “on neutral ground” to try to end the 40 year long conflict between the two countries.
If taken up it would be the first meeting in half a century between the leaders of Cuba and the US. The head of the Communist regime and a US president have not come face to face since the island’s revolution in 1959.
Fidel Castro’s offer to meet came with a warning for Mr Obama.
“He should remember the carrot-and-stick approach will not work with our country,” he wrote. “The sovereign rights of the Cuban people are not negotiable.”
Mr Obama has said he is open to talks with the Cuban government, and will consider easing Us sanctions. After taking office in January, he plans immediately to lift all restrictions on family travel and financial remittances to the island.
However he said he would not support lifting the four decade old trade embargo until Cuba releases all political prisoners. An independent human rights group has said that there are 219 prisoners of conscience on the island.
Before the US elections last month, Fidel Castro praised Mr Obama as intelligent and humanitarian.
Raul, who replaced his ailing brother in 2006, has said several times he was willing to talk to the US.
In his most recent interview, with left wing actor Sean Penn in the US magazine The Nation, he suggested they meet in Guantanamo Bay, the site of the prison camp and where the US maintains a naval base considered by Cuba as a violation of its sovereignty