Cuba freed some leading dissidents on Wednesday after holding them overnight to thwart an unauthorised demonstration in a crackdown that has tested its new detente with the United States.

Police arrested several political opponents on Tuesday and kept others under virtual house arrest ahead of an open microphone protest that was to have taken place outside the communist government headquarters in Havana's Revolution Square.

The detentions were typical of how Cuba breaks up opposition protests but took on greater significance coming just two weeks after US President Barack Obama and Cuban President Raul Castro said on December 17 they would restore diplomatic ties and end decades of hostility.

Among those released on Wednesday was performance artist Tania Bruguera, who organised the demonstration. After about an hour of freedom, she was picked up again by police and lectured for about two-and-a-half hours, she said.

Between her back-to-back detentions, she told Reuters in an interview that she planned to hold a similar, scaled down event on the seafront near her mother's home. But as she walked toward it she was picked up by plainclothes officers for a second time.

The planned event never took place.

"I'm not doing this as a dissident, I'm doing it as a normal person," she said at her mother's apartment just minutes before her second arrest. "I'm not a counter-revolutionary, like they say. I'm from a revolutionary family. I'm going to continue the project."

A Cuban government official declined to comment.

One of the other high-profile detainees, Reinaldo Escobar, the husband of prominent dissident blogger Yoani Sanchez, was released late on Tuesday night.

The dissident Cuban Commission for Human Rights and National Reconciliation said more than 50 Cubans were detained and that about 10 of them were still being held on Wednesday night.

"At the same time the Cuban government is normalising its relations with the US government, it has not decided to normalise relations with the people of Cuba," said Elizardo Sanchez, who heads the commission.

"We don't think there will be a cause-and-effect relationship between renewing diplomatic relations with the United States and an improvement of human rights in Cuba."

Cuban officials do not reveal information about police activity, and Reuters could not verify the numbers of detentions.

Obama's policy shift on Cuba has drawn some opposition inside the United States, led by Cuban-American senators Marco Rubio and Robert Menendez.

They both criticised Obama anew after the detentions, arguing that Cuba now has even less incentive to improve its human rights record and asking how the president would respond.

The US State Department condemned the Cuban actions, but gave no indication they would derail a high-level visit to Havana in January for talks on restoring diplomatic ties.

Obama has said Cubans should not face harassment or arrest for expressing their views and that Washington will continue to monitor human rights on the island.

Castro applauded Obama for changing US policy but says Cuba will not change its one-party system.

He also warned two weeks ago that "virulent critics", including Cuban-Americans in the US Congress and Cuban exiles, would "do everything possible to sabotage the process, without ruling out provocative actions of any kind".

Under the deal with the United States, Cuba agreed to release 53 people described by Washington as political prisoners, but they have not yet been freed and dissidents complain they do not even know who is on the list.