"I was appalled when one of the people running for or about to run for the Republican nomination talked about Cuban refugees as potential terrorists," Clinton told Hispanic elected officials. "Apparently he doesn't have a lot of experience in Florida or anywhere else, and doesn't know a lot of Cuban-Americans."
Thompson, who is polling strongly among GOP primary voters and is expected to join the race soon, made the comment at a campaign stop Wednesday in South Carolina.
The actor and former Tennessee senator was criticizing an immigration bill in the Senate, contending it would make the country more vulnerable to terrorism.
"I don't imagine they're coming here to bring greetings from Castro. We're living in the era of the suitcase bomb," Thompson said. Fidel Castro is Cuba's leader.
A video clip of Thompson's remark immediately circulated on YouTube, leading him to post a note on his campaign blog saying he had been talking about Cuban spies entering illegally, not immigrants entering legally.
Responding to a query Saturday, one Thompson press aide, Burson Snyder, referenced that post Thursday in which Thompson said, "Our national security is too important an issue to let folks twist words around for a one-day headline. Cuban-Americans are among the staunchest opponents of illegal immigration, and especially so when its sponsored by the Castro regime."
All the major Democratic presidential candidates were at Walt Disney World for a forum sponsored by the National Association of Latino Elected and Appointed Officials.
Speaking to a group of about 100 supporters before the forum, New Mexico Gov. Bill Richardson promoted his status as the first Hispanic to run for president.
"I'm not running as a Latino candidate. I'm running as an American governor who is enormously proud to be Latino," he said to cheers.
A fluent Spanish speaker, Richardson called his supporters at the association "Mi gente, mi familia," — my people, my family.
Florida, which intends to hold its important primary Jan. 29, is more than 20 percent Hispanic. Many are Cuban-Americans, who traditionally have favored Republican candidates.
Earlier Saturday, Clinton addressed about 1,000 women at a fundraiser in Miami, one of five she scheduled on the final day of the April through June period.
The campaign has announced that Clinton will match or slightly exceed the $26 million she took in from January through March. Still, Clinton aides have predicted Democrat Barack Obama would outraise her this time.
At the Miami event, Clinton said she would have much work to do at the White House if she won election in 2008.
"After eight years of the Bush administration, we are going to be shocked by what we find," the New York senator and former first lady said. "Somebody said to me the other day if there was ever a time for a woman president it's now because we're going to have to do a lot of cleaning."
The women, many of who brought their daughters to the $100 per plate "Women for Hillary" breakfast, applauded wildly.
"Grab your buckets, grab your brooms," Clinton said. "We're going to have to do a clean sweep because there has been a culture of cronyism, corruption and incompetence."
The Republican National Committee responded that women will not support Clinton based on her position on major issues.
"If Hillary Clinton thinks women will support her candidacy simply based on her gender she is mistaken," RNC spokeswoman Amber Wilkerson said. "Women, like men, will vote for a candidate because they share their views, and Hillary's consist of higher taxes, bigger government and waving a white flag in the global war on terror."