(CNN) -- In a spirited Republican presidential debate, Mitt Romney went after his surging conservative rival Newt Gingrich over his record as U.S. House speaker in the 1990s and accused Gingrich of lobbying after getting out of government.
Gingrich angrily denied the lobbying accusation, accusing Romney of lying about the issue and seeming flustered by the persistent attack.
Pausing at one point to collect his thoughts, Gingrich said Romney had been "walking around this state saying things that aren't true."
Romney continued, though, later saying to Gingrich: "You could call it whatever you like, I call it influence peddling."
The exchange was the sharpest in the early part of the debate, the first of two in Florida this week ahead of the January 31 primary in the Sunshine State.
Responding to the opening questions in the debate sponsored by NBC News, the National Journal and the Tampa Bay Times, Romney repeated attacks on Gingrich that he has stepped up since Gingrich's victory in Saturday's South Carolina primary and rise in the recent polls.
"Members of his own congressional team after four years of his leadership, they voted to replace him," Romney said of Gingrich's time as House speaker from 1995 to 99. "This was the first time in American history that a speaker of the House has resigned."
Romney also said contracts from Gingrich's work for federal mortgage insurer Freddie Mac showed that Gingrich was hired by the chief lobbyist for the group.
Gingrich has said he was a consultant for the group, while Romney is trying to depict Gingrich's role as an influence peddler for the organization linked to the U.S. housing crisis.
"Freddie Mac was paying Gingrich $1.6 million while taking money from the American people," Romney said.
Gingrich accused Romney of making false statements, though he declined to specify particular falsehoods in Romney's opening salvo.
He denied paying a fine for a congressional ethics violation while he was speaker, saying it was reimbursement for "the cost of going through the process" of determining one problem in his case.
Coming off a solid victory in South Carolina, Gingrich has cut the lead held by Romney in Florida and also caught the former Massachusetts governor in a national poll released Monday.
Also taking part in Monday's debate were former Pennsylvania Sen. Rick Santorum, who is vying with Gingrich for conservative support, and libertarian champion U.S. Rep. Ron Paul of Texas.
When the topic turned to foreign policy, both Gingrich and Romney took hardline stances, advocating a military response against any Iranian effort to block the Strait of Hormuz. Gingrich also supported everything short of a military invasion to overthrow the Cuban government, trying to appeal to a strong Cuban-American community in Florida.
Paul, meanwhile, persisted in his policies to reduce U.S. military presence around the world, saying in response to Gingrich's Cuba remarks that "the Cold War is over."
Calling instead for opening relations with Cuba, he said: "It's not 1962 anymore."
"We don't have to use force and intimidation," Paul said to some applause from the debate audience.
On another issue of interest to Florida voters, both Gingrich and Romney called for bolstering the U.S. space program by soliciting commercial investment.
Gingrich said setting specific goals such as a permanent presence on the moon and then establishing prizes for meeting them would spur an "amazing" private sector response, while Romney advocated a collaborative approach involving commercial, government, military and educational support.
With the first three contests of the nominating process producing three different winners -- Santorum in Iowa, Romney in New Hampshire and Gingrich in South Carolina -- Florida is a key battleground and offers a different campaign landscape.
The number of Florida Republican voters exceeds the combined total in the previous three states, requiring a larger campaign organization and more money to buy advertising. Romney got a head start in the state over his rivals, and also is expected to receive a boost from early voting permitted in Florida.
According to the state, at least 53,000 ballots have been cast in early voting that started statewide on Saturday, and 475,000 people requested and were sent absentee ballots, with 180,000 filled out and sent back by last Wednesday.
Those absentee votes came in before Gingrich skyrocketed in the polls and won South Carolina's primary by a double-digit margin.
Overall, nearly 1.95 million people voted in the 2008 Florida GOP primary.
According to the latest results from Gallup's daily tracking poll, Gingrich is in a statistical tie with Romney nationally among registered Republicans.
The national poll showed Romney at 29% and Gingrich at 28%. After the New Hampshire primary earlier this month, Romney was at 37% support and Gingrich at 14% in the same poll.
Monday's poll results showed Paul
Paul took part in Monday's debate but otherwise is not spending much money or time in Florida.
With little chance of winning, Paul chose not to compete in state where first place gets all the delegates. Instead, Paul is focusing on upcoming caucuses in Nevada, Colorado and Minnesota.
Before Monday's Florida debate, Romney ramped up his criticism of Gingrich, labeling him a Washington insider lobbyist, questioning his leadership, and demanding he release records tied to both a previous ethics investigation and work done for housing giant Freddie Mac.
Romney also demanded Gingrich return roughly $1.6 million earned from a contract with Freddie Mac, and ridiculed Gingrich's insistence that the work amounted to little more than "strategic" advice, as opposed to lobbying.
Earlier in the day, Gingrich said he had asked his former company, the Center for Health Transformation, to release the details of its consulting contract with Freddie Mac.
The latest maneuvering occurred against the backdrop of a GOP nomination fight that has changed dramatically over the course of the past week.
Initially announced as the victor in the January 3 Iowa caucuses by eight votes over Santorum, Romney learned Thursday that certified results showed Santorum actually won the state by 34 votes. Then came Gingrich's solid victory Saturday in South Carolina, in a race that Romney had led until his uncertain handling of whether to release his tax returns and a pair of debates widely considered to have been won dominated by the former speaker.
For his part, Gingrich on Sunday dismissed Romney's continuing critique of Gingrich's previous ethics controversy. The former speaker characterized a $300,000 penalty leveled by the House Ethics Committee in the late 1990s as reimbursement for the cost of the investigation.
He also claimed that he persuaded fellow Republicans in the House of Representatives to vote "yes" on the ethics charges against him in order to put a swift end to the proceedings.
According to the nonpartisan fact check group PolitiFact, Gingrich was reprimanded by the House and ordered to pay the $300,000 penalty in 1997 for violating an ethics rule. It noted that the penalty was considered reimbursement for the investigation.
The violation originated in a course Gingrich taught at Kennesaw State College, which organizers claimed qualified for tax-exempt status, PolitiFact reported. The House Ethics Committee ultimately concluded the course was run to "help in achieving a partisan, political goal," making it ineligible for tax exemption, according to PolitiFact.
Central to the 1997 investigation was a letter submitted by Gingrich's lawyers, which the ethics panel deemed inaccurate. Gingrich conceded Sunday the letter was a mistake.
CNN's Paul Steinhauser and Ashley Killough contributed to this report.
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