Cuba has released 2,991 prisoners in recent days under a New Year's amnesty announced by the president last Friday.
Council of State decree number one, signed by the president, Raul Castro, and dated Friday, issued final and unconditional pardons for the thousands of prisoners whose names were published in the government's Official Gazette on Wednesday.
Castro said the deal was a "humanitarian gesture" and had also "taken into account" an upcoming papal visit and requests by, among others, senior Roman Catholic Church officials in Cuba and relatives of the prisoners.
"We estimate that more than 2,500 prisoners have been released in all the provinces, and the process continues," Elizardo Sanchez, who heads the independent Cuban Commission on Human Rights, told the Reuters news agency on Tuesday.
Castro said on Friday the amnesty covered people more than 60 years of age, prisoners who are ill, women and some young prisoners who had no previous criminal history, as well as a few prisoners who had been convicted for crimes against "the security of the state."
Castro said 86 foreigners from 25 countries convicted of committing crimes in Cuba were also on the amnesty list. Seven political prisoners have reportedly been freed.
According to Sanchez's group, the dissidents pardoned were Alexis Ramirez Reyes, Modesto Alexei Martinez Torres, Carlos Martinez Ballester, Walfrido Rodriguez Piloto, Yordani Martinez Carvajal, Yran Gonzalez Torna and Augusto Guerra Marquez.
A number of Western diplomats said on Tuesday they were waiting to be contacted by Cuban authorities about their nationals in Cuban jails.
"The Cuban Commission on Human Rights applauds these releases, but really it is a limited gesture as we calculate there are between 70,000 and 80,000 Cubans in prison," Sanchez said.
He also told the AFP news agency that many prisoners on Monday protested in their cells around the country, as they learned about the amnesty deal, and that their names were left off.
One of the most surprising protests took place in Boniato, in Santiago de Cuba province, where "about 10 prisoners sewed their mouths shut and went on hunger strike", Sanchez said.
Some smaller demonstrations were reported at other prisons including Cuba's biggest, Combinado del Este, in the capital Havana, Sanchez said.
In 2010, Cuba released 130 political prisoners in a deal brokered by the Catholic Church.
Cuban dissidents have said there are still at least 60 people behind bars for political reasons, including some convicted of boat and plane hijackings and spying.