Hundreds of Cuban-Americans scrambled to board flights from Miami to Havana a day before new US restrictions on travel to the island came into force.
Most Americans cannot go to Cuba without special permission
The new US rules will only allow Cuban-Americans to visit relatives for two weeks once every three years in a bid to tighten an embargo on the island.
Last week, the US Treasury announced a grace period, saying anyone making it to Cuba now could stay until 1 August.
But there were not enough airline seats for everyone wanting to make the trip.
Some charter companies tried to put on extra flights to take advantage of the grace period, but the US State Department refused to approve additional trips from Miami.
Some 200 people staged a noisy protest at Miami International Airport. "We want to fly!" and "Cuba! Cuba," they chanted.
"The whole world can travel to their countries whenever they want, but we can't," said Jorge Luis Rodriguez, who wanted to visit his sick 81-year-old mother in Havana.
In Cuba, Justo Garcia was preparing to return to the US having visited his seven siblings and his 103-year-old grandmother.
"It's not easy to look at an elderly woman of 103 and say goodbye, not knowing if you'll ever see her again," he was quoted by the Associated Press as saying.
Under the new rules, Cuban-Americans can only visit direct family every three years, instead of every year.
They will be only be allowed to visit for 14 days, instead of previously unlimited stays. A daily spending limit has been reduced to $50 (£27) from $167 (£92).
US President George W Bush ordered the measures in May, calling them "a strategy that says we're not waiting for the day of Cuban freedom, we are working for the day of freedom in Cuba".
Supporters welcomed the restrictions, saying they would deprive Fidel Castro's communist government of vital tourism dollars.
Critics, including dissident groups on the island and Cuba's Roman Catholic bishops, say the moves will hurt only ordinary Cuban families who depend economically on the visits by relatives.
The US State Department had previously said that those already visiting Cuba must return before 30 June.
But because of a scarcity of return flights, the US government decided to extend the deadline by a month.