"We keep on thinking we've dispelled this," he said. "And it keeps on getting raised once again."
He said critics suggest "maybe he hasn't proven that he can win white blue-collar workers."
"And we won that in Virginia, and we won it in Wisconsin," he said.
In each new primary, he said, "we seem to have to prove this stuff all over." Given his wins, he said, "at this point, we should have put to rest this notion that somehow I am a candidate that's just focused on one demographic."
In handily winning the Mississippi primary on Tuesday, Obama took about 90 percent of the black vote and 30 percent of the white vote, according to exit polls. Similar results in other Deep South states have raised questions of whether Obama's strong black support is nudging some white Democrats into Clinton's column.
There was some evidence of that in exit polls in Ohio, which Clinton won. Analysts say a similar pattern could emerge in Pennsylvania, the next primary, on April 22.
Obama said he did not think the Clinton campaign was deliberately stirring racial divisions. He said, however, "I do think that the Clinton campaign has talked more during the course of the last few months about what groups are supporting her and what groups are supporting me, and trying to make the case that the reason she should be the nominee is there are a set of voters that Obama might not get. That seems to track certain racial demographics. And I disagree with that."
Obama said some voters might favor or disfavor him because he is black, just as some might favor or disfavor Clinton because she is female.
However, he said, "the overwhelming majority of Americans are going to make these decisions based on who they think will be the best president. I have absolute confidence that if I'm doing my job, if I'm delivering my message, then there are very few voters out there that I can't win."
"If I'm not winning them over," he said, "then it's my fault."
The Illinois senator opened the event flanked by nine retired military officers who said he is fully capable of being commander in chief, a response to Clinton's suggestions that he is unready and untested.
Retired Air Force Gen. Tony McPeak praised Obama for opposing a "dumb war" in Iraq. He said Obama has the steady temperament a leader needs, and called him "No-Shock Barack, No-Drama Obama."
At the 45-minute session with reporters at the Chicago Museum of History, Obama couched his criticisms of Clinton in fairly gentle terms.
He gently mocked her suggestion that he cannot win large states that will be key battlegrounds in November. He noted he won the Democratic primaries in Wisconsin, Missouri, Colorado, Iowa and Virginia, all of which should be fiercely contested this fall against Republican John McCain.
As for Clinton's victories in California and New York, Obama said, any Democratic nominee, including himself, should win those states handily.