By Matt Spetalnick, David Adams and Lesley Wroughton

WASHINGTON/HAVANA (Reuters) - Cuba has completed the release of all 53 prisoners it had promised to free, the Obama administration said on Monday, a major step toward détente with Washington.

The release of the remaining detainees overcomes a big hurdle for historic talks next week aimed at normalizing ties after decades of hostility. The list of 53 is part of last month's breakthrough U.S.-Cuba agreement and includes many known to international human rights groups as "prisoners of conscience."

The United States welcomed Cuba's action as a milestone, but senior U.S. officials said Washington would keep pressing Havana to free more people they consider political prisoners.

Lifting the secrecy around the freed dissidents, the Obama administration provided the full list to congressional leaders. According to a copy obtained by Reuters, they include members of prominent Cuba protest groups including the Ladies in White.

There had been questions whether Havana would release all those it had pledged to free as part of the deal that Presidents Barack Obama and Raul Castro announced on Dec. 17 to restore diplomatic ties, which Washington severed more than 50 years ago.

The mystery that surrounded the 53 had played to Obama's critics who say he has not pressured Havana enough on human rights in return for normalizing ties. The United States exchanged three convicted Cuban spies for an agent who had spied for the Americans. Washington also received Alan Gross, a U.S. aid worker jailed in Cuba.

Cuba informed the Obama administration over the weekend that the last of those on the list had been released, according to the officials, who spoke to Reuters on condition of anonymity.

But one of the officials said: "We’re going to be wanting to raise the cases of different individuals who may be detained in Cuba for exercising their universal rights."

Cuba denies that it holds political prisoners.

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LIST INCLUDES KNOWN DISSIDENTS

Jose Daniel Ferrer, leader of the peaceful opposition group Patriotic Union of Cuba, thanked the United States for helping to secure freedom for some of its members but said "we regret there are some political prisoners - about 10 - who remain in prison."

Among those on the release list were people designated by Amnesty International as "prisoners of conscience" such as brothers Bianco Vargas Martín and Diango Vargas Martín, members of the Patriotic Union arrested in 2012 and sentenced on public disorder charges to four years in prison.

Also listed were Haydee Gallardo, a member of Ladies in White, and her husband, Angel Figueredo, who were arrested last year.

The U.S. officials said as many as eight people on the list had been released even before the December announcement, some because they were already scheduled to get out. But a Cuban dissident leader said 17 of the 53 had been freed by that time.

Republican U.S. Senator Marco Rubio, a leading critic of Obama's policy, told CBS the release was great news for the prisoners but that Cuba was getting much of what it wanted from the administration in return for "these minimal changes."

Speaking in detail on the prisoner release for the first time since last month’s dramatic shift in Cuba policy, the U.S. officials said the idea grew out of secret talks on how to release Gross and how to structure the spy swap.

As both sides began seeing prospects for a broader rapprochement, U.S. negotiators sought proof of Cuba’s readiness to improve its human rights record and last spring presented a list of prisoners they wanted released, the officials said.

The Cubans agreed to almost everyone on the list with the exception of a handful. In July, they told Obama's aides that Havana was prepared to release 53 prisoners, the officials said. A final meeting was held at the Vatican and then the broader deal was rolled out in December after 18 months of negotiations.

One U.S. official also said Obama could exercise executive powers "in a matter of days and weeks" to begin easing some business and travel restrictions The officials said the first of those changes could be announced around the time of the Jan. 21-22 talks in Havana, when U.S. Assistant Secretary of State Roberta Jacobson begins high-level negotiations.

Reopening the U.S. embassy in Havana for the first time in 53 years will also be a "near-term" focus for the administration, but there is no timeline, one official said."You don’t erase decades of mistrust overnight but you can chip away at it," the official said.

With a Republican-led Congress unlikely to heed Obama's call to lift the longstanding U.S. embargo on Cuba, the official said: "We’re not counting on legislative proposals rolling through in the very near future." But the official expressed hope that over time "specific pieces" might win approval.

The United States used information from dissidents and rights groups to compile names of those who had peacefully exercised freedom of expression and assembly.

Left out, however, were the at least eight Cuban exile militants jailed on terrorism charges after they attempted to infiltrate Cuba with weapons, as well as 20 Cubans jailed on charges of attempting to hijack boats or planes.

Also excluded, U.S. officials said, were several Cubans jailed on unspecified charges of crimes against the state. They are believed to include a handful accused of spying for the United States, such as Ernesto Borges, a KGB-trained counter-intelligence officer who has been in prison for 16 years.

(Additional reporting by Patricia Zengerle in Washington and Dan Trotta in; Editing by Jason Szep and Frances Kerry)