(Adds debate response paragraphs 12-13, McCain quotes, paragraphs 17-18)
By David Wiessler
WASHINGTON, April 27 (Reuters) - Barack Obama, struggling to win over more white Democratic voters, said in a Sunday television interview race would not be a factor in November's election that could make him the first black U.S. president.
"Is race still a factor in our society? Yes. I don't think anybody would deny that," Obama said on "Fox News Sunday."
"Is that going to be the determining factor in a general election? No, because I'm absolutely confident that the American people -- what they're looking for is somebody who can solve their problems," the Illinois senator said in an interview taped on Saturday.
Obama and Democratic rival New York Sen. Hillary Clinton were focusing on Indiana, which with North Carolina will be the next big tests on May 6 toward picking a presidential nominee to face Republican John McCain in November.
Obama is leading Clinton in the popular vote, states won and committed delegates to the party's nominating convention in August, but her recent victories in Pennsylvania and Ohio have raised questions about his ability to win white voters.
In Pennsylvania, Clinton won white union households and white Catholics -- two important Democratic blocs -- by about 70 percent to Obama's 30 percent. About one in seven Pennsylvania voters said race was an issue and that group voted overwhelmingly against Obama.
Obama said he had won many of those same voters in other states and after a Democratic nominee was decided, they would back the party's candidate against McCain.
"I am confident that when you come to a general election, and we are having a debate about the future of this country -- how are we going to lower gas prices, how are we going to deal with job losses, how are we going to focus on energy independence -- that those are voters who I will be able to appeal to," he said.
"If I lose, it won't be because of race," Obama said. "It will be because ... I made mistakes on the campaign trail, I wasn't communicating effectively my plans in terms of helping them in their everyday lives."
Howard Wolfson, Clinton's top campaign strategist, agreed the party will be united against the Republicans once there is a Democratic nominee. Some Democrats fear the current fight could cause a dangerous split in the autumn.
"Both the Obama campaign and the Clinton campaign are absolutely committed to coming together at the conclusion of this process, coming behind whoever the nominee is, and enthusiastically supporting that person," he said on "Face The Nation" on CBS.
Clinton, a former first lady who would be the first female president of the United States, had challenged Obama to a one-on-one debate without moderator before the Indiana vote.
Obama turned her down to concentrate on meeting voters but said on Sunday he would be "more than happy to consider" another debate after Indiana.
Obama's comments on race came as his former pastor, Jeremiah Wright, began a series of public appearances to combat criticism of his controversial sermons that have, among other things, suggested the United States deserved some blame for the Sept. 11 attacks.
Obama again denounced Wright's offensive comments but said, since he had a long relationship with the pastor, voters had a legitimate interest in him. "I don't think that the issue of Reverend Wright is illegitimate," Obama said. "I just think that the way it was reported was not ... a reflection of both that church that I attend and who I am."
In Miami, McCain, the presumptive Republican nominee, said that while he had not commented on the controversy he is disturbed by some new remarks he has heard about.
"Senator Obama himself says it's a legitimate political issue, so I would imagine that many other people will share that view and it will be in the arena," he said at a news conference. "But my position that Senator Obama doesn't share those views remains the same."
Obama's appearance on "Fox News Sunday" came after host Chris Wallace started running a clock showing how long it had been since the Illinois senator said he would appear on the show -- 772 days up to Sunday.
"It takes me about 772 days to prepare for these questions," Obama joked as he opened the show.
Many Democrats say Fox is too conservative and Republican-oriented and some have refused to appear on the network. (Additional reporting by Tom Brown; Editing by John O'Callaghan) (To read more about the U.S. political campaign, visit Reuters "Tales from the Trail: 2008" online at blogs.reuters.com/trail08/)