Huckabee said: "Am I quitting? Let's get that settled right now. No, I'm not."
"We won north, we won south and we won in between," Obama later said at a party dinner in Richmond, Virginia, referring to his victories.
"The Democratic Party must stand for change, not change as a slogan, change we can believe in. That is what this campaign it all about."
With 34 per cent of precincts reporting in Louisiana, Obama won 54 per cent of the vote to 38 per cent for his rival Hillary Clinton, Fox News and CNN said.
Louisiana has some 56 delegates up for grabs as well as 10 superdelegates who can vote for whomever they like.
The Democratic party's race has been closely tied between the two nominees.
Clinton, New York senator, and Obama, Illinois senator, are about even in pledged delegates but well short of the 2,025 needed to win nomination.
Obama was the favourite in all three contests.
Among Republicans, Mike Huckabee, a former Arkansas governor, won contests in Louisiana and Kansas, dealing setbacks to John McCain, the frontrunner, two days after the Arizona senator had all but sewed up the nomination.
"This race is far from being over," Huckabee said after crushing McCain in Kansas.
|Huckabee says he is not quitting the presidential race [AFP]|
Two days earlier, McCain became the all-but-certain nominee with the withdrawal of his chief rival, Mitt Romney, a former Massachusetts governor.
Huckabee and McCain were running close in partial returns in Washington, which also voted on Saturday.
McCain has gathered more than 700 of the 1,191 delegates needed to win the Republican nomination at this summer's nominating convention.
But McCain still faces widespread opposition from conservatives unhappy with his views on immigration, tax cuts and other issues.
The win for Huckabee followed a strong showing in the South earlier in the week, when the Baptist minister won four Southern states and West Virginia in Super Tuesday voting that involved nearly half of the American states.
Obama and Clinton both campaigned in Maine, which has a contest on Sunday, and will appear on Saturday night at a Virginia Democratic party fundraising dinner.
Virginia votes on Tuesday.
During her stop in Maine, Clinton took aim at McCain and touted herself as the Democratic candidate with the experience to beat him in November.
"I can go toe-to-toe with Senator McCain on national security," she said.
Huckabee took a veiled swipe at Clinton at the conservative meeting, noting that in Arkansas, he was "the only person who's ever run against the Clinton political machine and beat it".
Clinton's husband, former US president Bill Clinton, preceded Huckabee as Arkansas governor.