The OAS Secretary General was supposed to attend an Oswaldo Paya award ceremony in Havana on Wednesday.
"My presence at the ceremony of the 22nd of February is no different from other similar events that take place in other countries of the region and in which I have participated," Almagro stressed in his letter.
Cuba has also denied entry to Mexico’s former president Felipe Calderon, who was also supposed to take part in the Oswaldo Paya award ceremony.
Oswaldo Paya was the founder of the Christian Liberation Movement that called for multi-party democracy in Cuba. He died in a car crash in 2012.