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U.S. officials believe Cuban President Fidel Castro has backed down from his threat to unleash a mass exodus of refugees. But contingency plans nevertheless are in the works.

"We've made very clear to Castro that he cannot dictate our immigration policy," White House chief of staff Leon Panetta said Sunday.The White House hopes to avoid a replay of the 1980 Mariel boatlift that dumped 125,000 Cuban refugees on south Florida shores. That specter was raised Friday when Castro blamed the United States for encouraging a recent exodus. He threatened to allow free emigration.

"We will not accept the threats that he's made with regards to trying to recreate what happened in the Mariel escape that took place a few years ago," Panetta said on NBC's "Meet the Press."

Asked how the United States would respond to an exodus and whether Cubans would be turned back, Panetta said: "I don't think we have to face that right now because, frankly, things are calming down. Castro has backed off of his threat. We do think that the situation - both in Miami as well as in Cuba - is now calm."

On Saturday, Castro said in Bogota, Colombia, that he still has the backing of most Cubans.

"It's true there's discontent among some people. But you have to consider the immense patriotism in most of the population, who understand the reasons for our problems and who are committed to the defense of the nation, the revolution and socialism," he said.

In Havana Sunday, hundreds of thousands of Cubans gathered at Revolution Square to show support for the government, two days after street clashes in the capital that injured 35 people.

The crowd, estimated by officials at 600,000, jammed the vast square at a meeting called to pay tribute to a policeman killed in a ferry boat hijacking but also to issue a firm rebuff against the unrest.

At a White House meeting Saturday, senior administration officials discussed a plan under development by the federal government for the past 13 years that lists the duties for various agencies responding to a Mariel-like crisis.

An administration official, speaking on condition of anonymity, said one of the options includes a blockade by U.S. warships of the passage between Key West, Fla., and Cuba. The official said Clinton has made no decisions on the idea, and reiterated Panetta's assessment of Cuba as calming.

Thousands of Cuban exiles chartered fishing boats in 1980 to bring their relatives and friends from Mariel, Cuba, to Key West.