(Adds quotes from freed rapper, details)

By Daniel Wallis

HAVANA, Jan 9 (Reuters) - One of Cuba's most prominent dissident groups said on Friday that 36 opposition activists, including a popular hip-hop artist, have been freed in the last two days as part of a deal to improve relations between Cuba and the United States.

The dissident Patriotic Union of Cuba (UNPACU) said 29 of its members were among those released, and that most had been warned by the communist government they would be sent back to prison if they continued their opposition activities.

"Our freed prisoners are committed to continue fighting for the democratic Cuba which we all want," UNPACU's leader Jose Daniel Ferrer said in a statement.

"The UNPACU activists have left prison with more energy, force and motivation than they had when they were jailed."

Cuba's commitment to free a list of 53 prisoners was a key part of the historic deal announced on Dec. 17 under which the Cuban and U.S. governments agreed to renew diplomatic relations after more than 50 years of hostilities.

Most of those released over the last two days were accused of such offenses as resisting arrest and threatening police officers, and had been given short sentences of two to five years.

The hip-hop artist, Angel Yunier Remon, known as "The Critic", was serving the longest prison term, eight years.

Remon was arrested in 2013 after painting a giant slogan, "Down With The Dictatorship!", on the street outside his home in the eastern city of Bayamo. He staged several hunger strikes while behind bars, and said he contracted cholera due to the unsanitary prison conditions.

"I'm so happy to be back with my family, my children, and my wife," Remon told Reuters by telephone from Bayamo on Friday morning, adding that he had no plans to give up working for the opposition.

"Our country is still a dictatorship," he said. "We're going to keep battling for an independent and truly free Cuba."

Dissident groups say most of those freed over the last couple of days have been released on the condition that they report regularly to the authorities.

Cuba's government does not comment on police actions involving detentions, and it has said nothing about this week's releases. It typically describes dissidents as "mercenaries" in the pay of the United States.

The top U.S. diplomat for Latin America, U.S. Assistant Secretary of State Roberta Jacobson, is due to visit Havana on Jan. 21-22 for talks with Cuban officials on the normalization of diplomatic ties and migration issues. (Reporting by Daniel Wallis; Additional reporting by Marc Frank; Editing by David Adams and Kieran Murray)