Nearly three-fourths of Americans think the United States should have diplomatic ties with Cuba, but they're not sure how far to go in lifting sanctions, according to an Associated Press-GfK poll released Monday, as full diplomatic relations between the two countries were formally restored.

"Relations between Cuba and the U.S. I think are long overdue. There's no threat there," said Alex Bega, 30, of Los Angeles. He added, "I think the sanctions we have on them are pretty much obsolete."

The resumption of normal ties ended decades of acrimony between the two nations that was hardened when President John F. Kennedy and Cuba's Fidel Castro fought over Soviet expansion in the Americas. The new diplomatic status, however, does not erase lingering disputes, such as mutual claims for economic reparations, Havana's desire to end the more than 50-year-old trade embargo and the U.S. push for Cuba to improve human rights and democracy. The new poll also found that 58 percent of Americans approve of President Barack Obama's handling of the U.S. relationship with Havana, while another 40 percent disapprove. By contrast, only 39 percent approve of his handling of the U.S. role in world affairs more generally, while 59 percent disapprove. Respondents were split on what to do about the sanctions on Cuba. Around 48 percent thought they should be decreased or eliminated entirely, while 47 percent favored keeping them at their current level or increasing them. Five percent didn't answer.

However, the story was different when it came to Iran. Some 77 percent said they thought sanctions on Tehran should be kept where they are or increased, according to the poll, which was conducted just days before the U.S. signed an agreement to curb Iran's nuclear program in exchange for economic sanctions relief. Under the agreement, Iran's nuclear program will be curbed for a decade in exchange for potentially hundreds of billions of dollars' worth of relief from international sanctions.

The U.S. and Cuba announced that they had started the normalization process in December 2014 to cooperate and improve formal diplomatic relations. In April, the pair held a historic first meeting in Panama after 54 years. The normalization process included the opening of embassies in each other's countries, a breakthrough prisoner exchange and easing of restrictions on commerce. Last week, JetBlue, a budget-friendly airline, added direct flight service from JFK Airport in New York City to Havana, and the world's largest cruise shipping company, Carnival Corp, said it has received approval from the U.S. government to offer trips to Cuba from Miami, which is expected to start early next year.