After taking office last year, Obama pledged to recast relations with his communist neighbour.
But hopes for warmer ties have dissipated over remaining US trade restrictions, spying and human rights.
Cuba has accused the Obama administration of continuing to meddle in its affairs by supporting and funding dissident groups in the same way as previous US governments.
"During the course of the past year, I have taken steps to reach out to the Cuban people and to signal my desire to seek a new era in relations between the governments of the United States and Cuba," Obama said.
"I remain committed to supporting the simple desire of the Cuban people to freely determine their future and to enjoy the rights and freedoms that define the Americas," he said.
A series of recent marches by against a group female protesters known as Las Damas de Blanco (the Ladies in White) in Havana, the capital of Cuba, were disrupted by pro-government protesters and police.
The rough tactics and arrests brought fresh international condemnation for the Cuban government, already under fire for the February 23 death of Zapata after an 85-day hunger strike in protest at prison conditions.
Zapata's protest did not end with his death on February 24.
The following day, Guillermo Farinas, another dissident, took up his cause, refusing food and water to protest against the treatment of 26 political prisoners in need of medical attention.
Farinas was taken to a local hospital from his home in Santa Clara, 280km east of the capital Havana, after he passed out on March 11, and is being fed intravenously.
The Cuban government deems Farinas "an agent of the United States" and his protest "blackmail."
It has said he would be "entirely responsible" for his own fate should he die.
Cuba insists it keeps no political prisoners, only "mercenaries' in the pay of the US.