A day before tough new U.S. restrictions on travel to Cuba (search) went into effect, hundreds of Cuban-Americans scrambled to get onto packed flights Wednesday to visit their families in the communist nation.

Many were angry that there were not enough seats for them all.

At one point, about 200 people waited to check in at Miami International Airport (search), chanting, "We want to fly!" and "We must go to Cuba!"

"The whole world can travel to their countries whenever they want, but we can't," said Jorge Luis Rodriguez, who was trying to visit his sick 81-year-old mother outside Havana.

The new rules that begin Wednesday are part of the Bush administration's attempt to hasten the fall of Cuban President Fidel Castro (search), but they have also split the politically important Cuban exile community in an election year.

Some members welcomed the restrictions, saying they will deprive Castro of vital tourism dollars. Others complained that the rules will only hurt families.

The rules prohibit Cuban-Americans from visiting family on the island nation more than once every three years, instead of the current once a year. They also limit visits to 14 days and daily spending to $50 per person in Cuba. Before, there were no limits on the length of a visit, and people could spend $167 a day.

The U.S. Treasury Department (search) announced the rules in May. It decided last week to create a grace period so that people who were in Cuba by Tuesday could stay until Aug. 1.

Many charter companies tried to add extra flights from Miami to take advantage of the grace period, and Cuban-Americans rushed to buy tickets so that they could stay in Cuba for a month. But the U.S. State Department refused to approve the extra trips from Miami.

A State Department official, speaking on condition of anonymity, said the grace period was not done to boost travel to Cuba, but to ensure that Cuban-Americans already on the island could get back to the United States.

Eleven of the 16 flights scheduled to leave Miami International for Cuba on Tuesday departed without passengers because they had State Department approval only to bring back people from the island, airport spokeswoman Insom Kim said.

That angered many people at the airport who had hoped to get on one of the flights.

"The plane left with my seat empty and I'm still here. That isn't fair," Rodriguez said.

Another Cuban-American, Nelson Rodriguez, had returned from Cuba on Monday after he met a long-lost half sister for the first time.

"Now I've got to wait three years to see her again. And I'm just getting to know her," said Rodriguez, 42.

But supporters of the new rules said they would have a positive effect in the long term.

"What we're talking about is freedom for 12 million Cubans and not for an elite who can afford to travel there," said Ninoska Perez Castellon of the Cuban Liberty Council (search), a hard-line exile group.

She said President Bush has her support for re-election because he is trying to end "an oppressive regime and not play election politics."