Gingrich, speaking to more than 500 supporters Wednesday, accused some of the candidates in the GOP debate the night before of acting like seventh-graders, The Arizona Republic reported.
"The bickering last night was very harmful," he said.
The Republic noted many had called the former House speaker's performance in the debate his strongest of the campaign season.
While trailing in the polls and promising no quick leap to the lead, he said he would steadily gain on opponents to win the Republican presidential nomination.
"We're at a great crossroads of American history," Gingrich said.
If elected, he said, one of his first moves would be to kill President Barack Obama's healthcare law.
Gingrich told reporters before his speech every American should be able to obtain healthcare but didn't say how he'd bring that about.
He challenged Obama to seven three-hour debates.
"If he wants to, he can bring a TelePrompTer," Gingrich said.
Gingrich has garnered about 8.3 percent of support in polls, nearly tied with Ron Paul, but behind former Massachusetts Gov. Mitt Romney and ex-pizza company chief Herman Cain, who leads, and Texas Gov. Rick Perry, who's in third.
Gingrich, 68, is widely known for his role in the Contract with America, widely seen as spurring the Republican revolution that ended 40 years of Democratic control of Congress in 1994.