Two of the leading Republican voices on U.S. foreign policy have denounced President Barack Obama's plans to ease U.S. restrictions on Cuba.
Senators John McCain and Lindsay Graham claimed the move showed "America and the values it stands for in retreat and decline."
"It is about the appeasement of autocratic dictators, thugs, and adversaries, diminishing America's influence in the world," the pair said in a statement.
Freed aid worker Alan Gross said on Wednesday he was "very happy" to hear about the thaw in relations between the US and Cuba.
Speaking to the media after his release from Cuba, he thanked U.S. President Barack Obama for all he had done to secure his release and said he did not blame the Cuban people for his ordeal.
"Two wrongs never make a right. I truly hope that we can all get beyond these mutually belligerent policies and I was very happy to hear what the president had to say today," Gross said.
President Obama has announced a historic change in relations between the US and Cuba, ending 50 years of virtual separation between the two states.
But the move was met with hostility from some of his Republican opponents, who accused Mr Obama of rewarding a regime that suppresses its own population.
ITV News Washington Correspondent Robert Moore reports.
Pope Francis has congratulated the United States and Cuba on their decision to establish diplomatic relations, and the Vatican said it was ready to support the strengthening of bilateral relations.
In a statement, the Vatican also confirmed that its diplomats facilitated talks between the two countries, "resulting in solutions acceptable to both parties."
Three Cuban intelligence agents who had served 16 years in U.S. jails have returned to Cuba.
They were released as part of a prisoner exchange in which Cuba freed an American foreign aid worker who had served five years in a Cuban prison, President Raul Castro said.
Castro said he spoke with U.S. President Barack Obama by telephone on Tuesday ahead of the announcement that the United States would be moving to normalise relations between the two countries.
Cuban president Raul Castro has confirmed that his government will release a man of Cuban origin who had spied for the United States.
President Obama says today's announcement of moves to normalise US relations with Cuba is "the most significant change" in policy in over 50 years.
He said the "outdated" approach of cutting Cuba off from the US had not delivered for either country.
Among the moves will be the re-establishment of a US embassy in the Cuban capital, Havana.
The Vatican had a significant role in negotiations to release US prisoner Alan Gross from Cuba, according to a US Senator.
Dick Durbin, who represents the state of Illinois, has campaigned for Mr Gross' release and said he was "overjoyed" by the news.
But there were already quick objections to the news from some U.S. lawmakers.
Robert Menendez, the current head of Senate Foreign Relations Committee, denounced President Barack Obama's actions on Cuba, saying they "vindicated the brutal behavior of the Cuban government."
U.S. Senator Marco Rubio said on Wednesday he would "make every effort" to block moves by President Barack Obama toward normalising relations with the Cuban government.
"The president's decision to reward the Castro regime and begin the path toward the normalization of relations with Cuba is inexplicable," Rubio said in a statement.
The Florida Republican senator, who is Cuban-American, said he would use his role as chairman of the Senate Foreign Relations Committee's Western Hemisphere subcommittee in the new Congress to try to block the plan.
The United States and Cuba are moving to "normalise" diplomatic relations after more than 50 years of separation, President Obama is expected to announce.
Senior U.S officials, previewing Obama's forthcoming announcement, said the United States and Cuba will move to open embassies in each other's capitals, Reuters reports.
President Obama spoke on Tuesday to Cuban President Raul Castro to discuss the changes in a call that lasted nearly an hour.
As part of the relaxation in relations, Secretary of State John Kerry is expected to review Cuba's status as a state sponsor of terrorism.
"These steps will be the most significant changes to our Cuba policy in more than 50 years," a senior administration official told reporters.
"What we are doing is beginning the normalisation of relations between the United States and Cuba."