HAVANA (CNN) -- Cuba and Nicaragua have engaged in a sarcastic war of words in recent days over some 200 asylum-seekers who escaped the communist-run island in flimsy boats earlier this year but were repatriated from the Bahamas last month.

Nicaragua's President Arnoldo Aleman offered asylum to the group, which includes four Cuban baseball players, saying the would-be exiles were merely seeking "freedom."

Havana rejected the offer and made a sarcastic counter-offer "if Mr. Aleman is so generous" to send to Nicaragua any other Cubans wishing to leave the island legally.

Aleman responded Monday by saying that Cuba's problems could "be easily resolved" if just two people -- President Fidel Castro and his powerful brother Raul -- took asylum in Nicaragua instead.

Diplomats in Cuba say the spat between the two countries is not surprising, given past enmity between them. The right-wing Aleman is an enemy of Castro, who has strongly supported Nicaragua's left-wing Sandinista movement.

Since the weekend, Cuban authorities have maintained tight security around the Nicaraguan Embassy in Havana's upscale Miramar district. Uniformed and plainclothes police officers have been guarding the road, and branches were chopped from trees just outside the compound to prevent anyone from climbing them to drop into the embassy grounds and ask for asylum.

Earlier, Cuban baseball players Angel Lopez, Jorge Diaz and Michael Jova and coach Orlando Chinea met with Nicaraguan officials at the embassy.

"They told us that the Nicaraguan Embassy and Cuban authorities were going to do everything possible to speed up the paperwork so we could leave soon for Nicaragua," Chinea said.

Cuba has pruned back the trees in front of the Nicaraguan Embassy in Havana

That turned out not to be true. And on Wednesday, Cuba called off scheduled tours to Nicaragua by its two main national baseball teams.

National baseball director Carlos Rodriguez told local state-run media that the political squabble did not create "a propitious climate" for the series of games the Cuban teams had planned for this month in Managua.

"Given the somewhat unrespectful decisions by the Nicaraguan authorities relating to the granting of visas to (Cuban) rafters and other dissidents from Cuba, a climate has emerged which does not favor at all going ahead with these encounters," Rodriguez said.

State news agency Prensa Latina condemned Nicaragua's "unrespectful treatment and lack of gentlemanliness."

The deportations of the Cubans from the Bahamas in May honored a 1996 immigration accord between Nassau and Havana. It reflected new efforts by the Bahamas not to become a way station for Cubans hoping to reach the United States.

Cuban exiles in Miami were angered. They said the escapees faced reprisals in their country and should have been treated as political refugees.