From Wednesday, the estimated 1.5 million Cubans living in the United States will have visits home and their right to send back remittances to families cut.
The move has angered many Cuban-Americans even though most are strong opponents of the Castro government. The Cuban authorities have called the measures "cruel".
On Tuesday there were not enough airline seats for scores of people trying to get flights back before the restrictions came into effect at midnight (04:00 GMT).
Some staged noisy protests at Miami airport shouting: "We want to fly!" and "Cuba! Cuba!"
"I came from Iraq," said Carlos Lazo, a Cuban-American who said he had served in the US army there. "And because of Mr Bush's policies, I cannot go to see my family," he added.
US President George Bush ordered measures to tighten the 42-year-old US embargo on Cuba in May. At the time he called it "a strategy that says we're not waiting for the day of Cuban freedom, we are working for the day of freedom in Cuba."
Under the move, Cuban-Americans can only visit direct family on the island every three years instead of every year. And these are now restricted to 14 days with daily spending of $50.
There was previously no time limit on the stays and spending of about $165 a day was allowed.
The US State Department had said that those in Cuba before the new restrictions must return by 30 June. But because of the crush on scarce return flights, the US government on Tuesday extended the deadline until 30 July.
Cuban emigres can still send $300 home every three months but only to immediate family and not to cousins, aunts and uncles. Government and communist party officials are also excluded from receiving the remittances.
"I came from Iraq.
And because of
Mr Bush's policies,
I cannot go to see my family ... This year I
will not vote for Bush"
Carlos Lazo, a Cuban-American who served in US army
According to the Inter-American Development Bank, remittances from US-based Cubans in 2002 were worth more than $1.1 billion and played a major role in keeping the Cuban economy alive.
But the US administration suspects much of the foreign currency entering Cuba is siphoned directly to Castro and his entourage.
About half of Cuban-Americans live in Florida and some see a political ploy by Bush ahead of the 2 November presidential election, in which he is in a narrow battle with Democratic contender John Kerry.
Cuban-American votes played a crucial role in Bush's controversial electoral victory in Florida in 2000, which decided his victory.
Lazo said he was proud to have served in Iraq, but added: "This year I will not vote for Bush."
The Cuban American National Foundation, one of the leading anti-Castro groups in the United States, has expressed doubts about the new measures.
What worries them most is the restricted ability to help families back in Cuba.
The foundation said in a statement that "the bonds of family, intrinsic in Cuban culture and nationality," enables the Cuban people to thrive and remain dedicated to the cause of seeking freedom and democracy.
Alberto Fernandez, who has been living in Miami since the 1980s, insists the Bush administration is right to put pressure on the Cuban government. But he disagrees with measures concerning Cuban families.
"For Cubans, families are the most important thing," he said.
Cuba's veteran revolutionary leader has led anti-US protest rallies since the new restrictions were announced, warning that the United States was planning an invasion.
But the government has also imposed new austerity measures, including price rises at dollar denomination stores, insisting its people heroically confront grim economic hardship.