Obama defended the mailings as accurate and rejected Clinton's complaint as a political ploy. He said that despite her current criticism of NAFTA, she supported the trade agreement when it passed during her husband's administration.
"You can't be for something and take credit for an administration ... and then when you run for president say that you didn't really mean what you said way back then. It doesn't work like that," he said to cheers at a rally in Akron.
The long distance clash erupted as the two Democrats campaigned separately across Ohio, one of two big states with primaries on March 4.
Obama has won 11 straight primaries and caucuses, and some of Clinton's supporters have said she must win both Ohio and Texas next week to keep her hopes alive of winning the party nomination. Recent polls show Ohio is close, and Texas closer.
Clinton's frustration was evident as she criticized Obama in unusually strong terms - a few days after ending a nationally televised debate by saying she was "honored to be here with" him in a historic race between a black man and a woman.
She said by his actions, Obama was giving "aid and comfort to the very special interests and their allies in the Republican Party who are against doing what we want to do for America."
"Meet me in Ohio," she said. "Let's have a debate about your tactics and your behavior in this campaign." The two are scheduled to debate next Tuesday in Cleveland.
In her criticism of Obama, she asked, "Since when do Democrats attack one another on universal health care?"
Obama had a ready reply to that. "Well, when she started to say I was against universal health care ... which she does every single day," he said.
Since late last year, Clinton has consistently attacked Obama's health care plan, saying it would leave 15 million Americans uninsured.
Clinton's advisers have repeatedly criticized the Obama campaign's mailings, both of which went out in the last several days.
One says her plan for universal coverage would "force" everyone to purchase insurance even if they can't afford it. Her plan requires everyone to be covered, but it offers tax credits and other subsidies to make insurance more affordable.
Obama's plan does not include the so-called "individual mandate" for adults, and he has argued that people cannot be required to buy coverage if they can't afford it. He has said his first priority is bringing down costs.
The Illinois senator's plan does include a mandate requiring parents to buy health insurance to cover children.
The second mailing, on the North American Free Trade Agreement, quotes a 2006 Newsday article suggesting Clinton believed the agreement had been a "boon" to the economy. NAFTA and other trade agreements are extremely unpopular in Ohio, which has suffered an exodus of blue-collar jobs to other countries in part due to such agreements.
It's a particularly sensitive matter for Clinton, whose husband championed and pushed for passage of the agreement as president. She is counting on the support of white, working class voters in the state.
"I am fighting to change NAFTA," she insisted. "Neither of us were in the Senate when NAFTA passed. Neither voted one way or the other."
Clinton said Newsday had corrected the record about her views on the agreement. Indeed, the paper published a blog item earlier this month saying Obama's use of the word "boon" was unfair.
"Obama's use of the citation in this way does strike us as misleading," the paper said. "The quote marks make it look as if Hillary said "boon," not us. It's an example of the kind of slim reeds campaigns use to try to win an office."
Earlier, Newsday published an item saying the word "boon" had been the paper's "characterization of how we best understood her position on NAFTA, based on a review of past stories and her public statements."
As evidence of their concern about the issue, the Clinton campaign released two new ads in Ohio, including one featuring John Glenn - a former astronaut and U.S. senator from Ohio for 24 years - saying Clinton would fix trade agreements like NAFTA.
Clinton said she felt good about her prospects in Ohio and Texas but refused to say whether she needed to win both states to stay in the race.
"Let's let the people of Ohio vote. Let's actually have an election and then we can look at the results," she said.
