The Washington Post and The St. Petersburg Times reported on Thursday that documents show Mr. Rubio’s family first arrived in the United States in 1956, two and a half years before Mr. Castro took power. In various television interviews over the years, Mr. Rubio gave various dates for his parents’ arrival, 1957, ’58 or ’59.

Until today, Mr. Rubio’s official Senate biography had stated that his “Cuban-born parents came to America following Fidel Castro’s takeover.”

“In hindsight, I wish I had found out about the dates,” Mr. Rubio said. “But it was not relevant to the important narrative about what my experience was.”

The idea that he embellished his family story for political advantage is “outrageous,” he added.

Senator Rubio, who rose to power last year with the blessing of the Tea Party, quickly caught the attention of national Republicans who see him as a young, alluring voice for the party who can also reel in Hispanic voters. Mr. Rubio’s immigrant success story — parents who were exiled from Cuba and worked hard to do right by him — is central to his political persona.

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It is far too early to tell what, if any, long-term political damage may befall Mr. Rubio’s national aspirations. Democrats, though, delivered their salvos right away.

“Marco Rubio has a chronic credibility problem,” said Matt Canter, a spokesman for the Democratic Senatorial Campaign Committee, in a news release. “We know he’s a Tea Partier who wants to dismantle Medicare and cut Social Security, but the latest bombshell confirms that Rubio seriously struggles to tell the truth and can’t be trusted.”

Republicans, including those who write political blogs and do not typically shy from criticizing their own, have been largely supportive.

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Mr. Rubio’s confusion over the precise facts of his family’s journey from Cuba to the United States does raise questions about his level of experience and whether he is prepared for the scrutiny of high-stakes national politics.

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“Is this a kill shot? No,” said Dario Moreno, an associate professor of political science at Florida International University and an ally of Mr. Rubio’s. “It’s something to attempt to damage his credibility and to make Marco seem like other politicians.”

But some Cuban-Americans wonder how Senator Rubio could have gotten the year of his parents’ arrival here so wrong. The date, they said, is integral to every exile story.

“Every Cuban-American knows when their parents arrived and the circumstances under which they arrived,” said George Gonzalez, a Cuban-American political science professor at the University of Miami. “That’s part of the Cuban exile experience, the political and psychological trauma of it. So the idea that he was murky on those does not cut ice.”

And while some Cubans do not draw a distinction between those who fled Cuba after Castro took power and those who left before that date, others do. “To my father and grandparents, if you came before the revolution, it puts you in a different category,” Dr. Gonzalez said.

But Cuban-exile politics are never cut-and-dried. Another expert at the University of Miami disagreed in a press release.

“The fundamental Cuban exile experience is not defined according to what year Cubans left, ” said Andy S. Gomez, an assistant provost and a senior fellow at the university’s Institute for Cuban and Cuban-American Studies, “but rather by the simple, painful reality that they could not return to their homelands to live freely.”