NEW YORK (CBSNewYork/AP) — The United States and Cuba have agreed to re-establish diplomatic relations and open economic and travel ties, marking a historic shift in U.S. policy toward the communist island after a half-century of enmity dating back to the Cold War.

The announcement comes amid a series of new confidence-building measures between the longtime foes, including the release of American Alan Gross, as well as a swap for a U.S. intelligence asset held in Cuba and the freeing of three Cubans jailed in the U.S. The deal was brokered in part by Pope Francis.

President Barack Obama announced the policy shift during a noon press conference Wednesday, saying the U.S. is ending its “outdated approach” to Cuba that has failed to advance U.S. interests.

“Isolation has not worked,” Obama said in remarks from the White House. “It’s time for a new approach.”

"These 50 years have shown that isolation hasn’t worked. It’s time for a new approach." —President Obama #CubaPolicy pic.twitter.com/dppjtoqGWP — The White House (@WhiteHouse) December 17, 2014

As Obama spoke, Cuban President Raul Castro was addressing his own nation from Havana, saying he welcomes the restoration of relations with the United States.

In a nationally broadcast speech, the Cuban leader said profound differences remain between Cuba and the U.S. in areas such as human rights, foreign policy and questions of sovereignty. But he said the countries have to learn to live with their differences “in a civilized manner.”

Obama and Castro spoke by phone for more than 45 minutes Tuesday, the first substantive presidential-level discussion between the U.S. and Cuba since 1961.

As part of resuming diplomatic relations with Cuba, the U.S. will soon reopen an embassy in the capital of Havana and carry out high-level exchanges and visits between the governments. The U.S. is also easing travel bans to Cuba, including for family visits, official U.S. government business and educational activities. Tourist travel remains banned.

Licensed American travelers to Cuba will now be able to return to the U.S. with $400 in Cuban goods, including tobacco and alcohol products worth less than $100 combined. This means the long-standing ban on importing Cuban cigars is over, although there are still limits.

The U.S. is also increasing the amount of money Americans can send to Cubans from $500 to $2,000 per quarter, or every three months. Early in his presidency, Obama allowed unlimited family visits by Cuban-Americans and removed a $1,200 annual cap on remittances. Secretary of State John Kerry is also launching a review of Cuba’s designation as a state sponsor of terror.

Obama does not have the authority to fully lift the long-standing U.S. economic embargo on Cuba, given that Congress enacted that policy. However, officials said he would welcome lawmakers taking that step.

Obama said he continued to have serious concerns about Cuba’s human rights record but did not believe the current American policy toward the island was advancing efforts to change the government’s behavior.

“I do not believe we can keep doing the same thing for over five decades and expect a different result,” he said.

There remains a divide on Capitol Hill over U.S. policy toward Cuba. While some lawmakers say the embargo is outdated, others say it’s necessary as long as Cuba refuses to reform its political system and improve its human rights record.

Sen. Marco Rubio, R-Florida, said the policy did nothing to address those issues.

“But it potentially goes a long way in providing the economic lift that the Castro regime needs to become permanent fixtures in Cuba for generations to come,” Rubio said.

High-ranking Cuban-American lawmakers in New Jersey are speaking out against the plans.

U.S. Senate Foreign Relations Committee chairman Robert Menendez, whose parents came to New York from Cuba just before he was born, called the release of Alan Gross “a moment of profound relief” for Gross’ family.

But he assailed the deal, saying “President Obama’s actions have vindicated the brutal behavior of the Cuban government.”

“Trading Mr. Gross for three convicted criminals sets an extremely dangerous precedent,” Menendez said. “It invites dictatorial and rogue regimes to use Americans serving overseas as bargaining chips. I fear that today’s actions will put at risk the thousands of Americans that work overseas to support civil society, advocate for access to information, provide humanitarian services, and promote democratic reforms.”

Assembly Speaker Vincent Prieto, a Cuban native who emigrated to the U.S. when he was 11, said Wednesday he fears normalizing relations will strengthen the Cuban regime and “cement its permanency.”

Prieto says he knows “first-hand” the Cuban regime’s poor record on human rights and its resistance to democracy.

In New York City, Mayor Bill de Blasio, who spent his honeymoon in Cuba, said the move was decades overdue.

“I think the president’s doing the right thing,” he said. “I think this is part of moving us forward, and I actually think it will help the democratization process in Cuba. The more the American example is there, I think the more chance that that country will democratize.”