Cuban President Raul Castro has hailed the mutual decision to re-establish the US-Cuban diplomatic relations, but urged Washington to lift the five-decade-long embargo against his country.
On Wednesday, the countries agreed to restore diplomatic ties that were severed more than 50 years ago, and US President Barack Obama called for an end to the economic embargo against its old Cold War enemy.
"President Obama's decision deserves the respect and acknowledgement of our people," Castro said in a televised address, while warning that the embargo, which he calls a "blockade", must still be lifted.
"We have agreed to re-establish diplomatic relations, but this does not mean the principal issue has been resolved: The blockade which causes much human and economic damage to our country should end," he said.
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He challenged Obama to modify the policy, which is rooted in US law, with executive action.
Obama said on Wednesday that the US was changing its relationship with the people of Cuba.
"We will begin to normalise relations between our two nations. Through these changes, we intend to create more opportunities for the American and Cuban people and begin a new chapter," he added.
Al Jazeera's Patty Culhane, reporting from Washington, said the trade embargo imposed on Cuba after ties were severed can only be lifted by Congress.
"Senior administration officials tell me they don't think Congress is going to lift the embargo. We have seen several members of Congress come out and call the president's moves 'outrageous'," she said.
Republicans, who will control both houses of Congress from January, oppose normal relations with the Communist-run island.
"Relations with the Castro regime should not be revisited, let alone normalised, until the Cuban people enjoy freedom - and not one second sooner," said House Speaker John Boehner.
1959: An armed revolt in Cuba led by Fidel Castro established a socialist state
1960: Cuba nationalised all American businesses, resulting in the US imposing an economic embargo
1961: The US attempted to overthrow Castro in a failed invasion at the Bay of Pigs
1962: The Cuban Missile Crisis almost led to a US invasion, after the Soviet Union deployed nuclear missiles in Cuba
2009: An easing of tensions when Barack Obama came to power and lifted some restrictions on travel and remittances to Cuba. But later that year US citizen Alan Gross was detained, which froze relations once again
"There is no 'new course' here, only another in a long line of mindless concessions to a dictatorship that brutalises its people and schemes with our enemies.''
A day earlier, after 18 months of secret talks, Obama and Castro agreed in a phone call on a breakthrough prisoner exchange, the opening of embassies in each other's countries, and an easing of some restrictions on commerce.
Havana released a US citizen, Alan Gross, who had been jailed for five years in Cuba, and an intelligence agent who had spied for the US and was held for nearly 20 years.
Cuba's jailing of Gross, convicted for importing banned technology and trying to establish clandestine internet service for Cuban Jews, had been a major obstacle in improving ties.
The US in return freed three Cuban intelligence agents who had served 16 years in US jails for spying on Cuban exile groups in Florida.
Castro said the Cubans' release was a cause of "enormous joy for their families and all of our people".
He also praised Obama for agreeing to the prisoner exchange and pushing for a new relationship with Cuba.
Castro thanked Pope Francis, the Vatican and Canada for helping Havana and Washington reach their historic accord.
Obama said he had instructed Secretary of State John Kerry to immediately initiate discussions with Cuba on the re-establishment of diplomatic relations with Cuba, which were severed in 1961.
"In the coming months, we will re-establish an embassy in Havana and carry out high-level exchanges and visits between our two governments as part of the normalisation process," Obama said.
Source: Al Jazeera and agencies