Catholic bishops in the U.S. and Cuba rejoiced at the historic announcement of a new relationship between the countries, while some U.S. leaders warned the policy shift could have negative consequences.

"Engagement is the path to support change in Cuba and to empower the Cuban people in their quest for democracy, human rights and religious liberty," said Bishop Oscar Cantú of Las Cruces, N.M., who chairs the U.S. bishops' Committee on International Justice and Peace.

In a Dec. 17 statement, he voiced joy and gratitude for the announcement of plans to normalize relations between the U.S. and Cuba, which have for decades been marked by an embargo and lack of formal diplomatic relations.

"Our Conference has long held that universal human rights will be strengthened through more engagement between the Cuban and American people," Bishop Cantú said.

"We believe it is long past due that the United States establish full diplomatic relations with Cuba, withdraw all restrictions on travel to Cuba, rescind terrorist designations aimed at Cuba, encourage trade that will benefit both nations, lift restrictions on business and financial transactions, and facilitate cooperation in the areas of environmental protection, drug interdiction, human trafficking and scientific exchanges."

The Cuban bishops also expressed their gratitude over the new policy in a statement, saying it opened "new horizons of hope" for the Cuban people.

The U.S. and Cuba announced a prisoner exchange and a new relationship between the countries on Dec. 17.

Discussions are in place for diplomatic relations between the countries to be reset for the first time in more than 50 years. In addition, a U.S. embassy in Havanna and high-level U.S. visits to the country are being planned.

The Cuban government released American Alan Gross "on humanitarian grounds" after his five-year imprisonment there, as well as a valuable U.S. intelligence "asset" imprisoned for 20 years whom Obama administration officials declined to name. The U.S. released three Cubans who were being held for espionage.

The Vatican was a major supporter of the exchange and the new relationship, the White House revealed, with Pope Francis personally appealing to leaders of both countries for a new policy. The Vatican hosted the final meeting where the exchange was made official, and senior Vatican officials participated in the talks – the only other country to take part in the discussions.

The Vatican released a statement late on Wednesday applauding the agreement.

"The Holy Father wishes to express his warm congratulations for the historic decision taken by the Governments of the United States of America and Cuba to establish diplomatic relations, with the aim of overcoming, in the interest of the citizens of both countries, the difficulties which have marked their recent history," read the statement from the Vatican Communiqué of the Secretariat of State.

"Pope Francis did what popes are supposed to do: Build bridges and promote peace," stated Archbishop Thomas Wenski of Miami, who called the new relationship "a real game changer."

"He acted much like his namesake, Francis of Asissi, who during the fifth crusade, went to Egypt to meet with the Sultan al Kamil in the interest of peace," he continued.

"The Church in Cuba has always opposed the embargo, arguing that it was a blunt instrument that hurt the innocent more than the guilty," he said.

Raul Castro has "seemed to indicate that his government was open to engage in conversations with the U.S. on issues related to democracy and human rights," Archbishop Wenski said. "Progress in this area is normally the result, and not the precondition, of such talks - and so the prospect of such talks is a positive development."

Not everyone embraced the announcement of the policy change, however. It drew strong criticism from Cuban-American senators on both sides of the political aisle, who warned that it could have disastrous consequences for people in both the U.S. and Cuba.

Sen. Marco Rubio (R-Fla.), a member of the Senate Committee on Foreign Relations, went so far as to call it a "victory for oppression."

"The entire policy shift is based on the illusion – in fact, on the lie – that more commerce and access to money and goods will translate to political freedom for the Cuban people. Cuba already enjoys access to commerce, money and goods from other nations, and yet the Cuban people are still not free," he said in a Wall Street Journal op-ed published Dec. 18.

Rubio warned that Obama had set a dangerous precedent of negotiating for hostages and had granted concessions to a government that imprisons political opponents and prevents free speech and free elections.

"The opportunity for Cuba to normalize relations with the U.S. has always been there, but the Castro regime has never been interested in changing its ways. Now, thanks to President Obama's concessions, the regime in Cuba won't have to change," he said.

The chair of the Senate's Foreign Relations Committee, Sen. Bob Menendez (D-N.J.), called the policy change "dramatic and mistaken," saying that it "fails to understand the nature of the regime in Cuba that has exerted its authoritarian control over the Cuban people for 55 years."

"It is a fallacy that Cuba will reform just because the American President believes that if he extends his hand in peace that the Castro brothers suddenly will unclench their fists," he warned.

"A majority of democratic activists on the island, including many that I have met with, have been explicit that they want the U.S. to become open to Cuba only when there is reciprocal movement by the Castro government."

Menendez observed that Cuba is losing its main benefactor with the collapse of the Venezuelan economy. Therefore, he said, offering the Cuban regime "an economic lifeline" at this time is simply perpetuating "the Castro regime's decades of repression."

He also cautioned against removing Cuba from the list of state sponsors of terrorism when the nation "harbors American fugitives" and has worked with North Korea in an effort "to smuggle jets, missile batteries, and arms through the Panama Canal."