Thompson campaigned in Iowa Friday.
(CNN) - Critical of Fred Thompson's decision to skip Wednesday night's Republican debate, Mike Huckabee sent a letter to the newest contender for the GOP presidential nomination on Friday encouraging him to participate in a one-on-one debate.
“Senator, let’s lead by example and get the ball rolling,” Huckabee, a former Arkansas governor, wrote Thompson.
Thompson, a former Tennessee senator, said in an interview on Fox News he would rather participate in a series of Lincoln-Douglas styled debates, where two candidates discuss a specific issue for at least an hour. Huckabee wrote to Thompson to "officially accept" his offer.
"I agree that what is needed is a real discussion by the candidates about their vision for the future of our country," Huckabee wrote.
On Thursday, Huckabee was critical of Thompson for skipping the debate and said he should have been shoulder-to-shoulder with the rest of the candidates.
"He has certainly sucked up a lot of the oxygen as it relates to media attention," the former Arkansas governor said in a conference call with reporters.
"I think it hurt him in New Hampshire, from the comments we've been hearing," Huckabee continued. "People don't like that he had an opportunity to launch his campaign in one of the early states where people take politics quite seriously.... and he chose not to do that."
Huckabee said Thompson's decision to enter the race won't affect his current campaign strategy, but he still went on to take a few subtle jabs at the former senator from Tennesee.
"It's not just that I've said conservative things,” Huckabee said. “I've done conservative things actually having run a government. I've never been a Washington lobbyist. I've never lobbied for an abortion rights group. If we want to compare authentic conservatism, I'll be happy to have not just my comments but my record compared to anybody who stood on that stage or anybody who didn't stand on that stage last night.
- CNN's Chris Welch and Lauren Kornreich