The Obama campaign responded with a statement suggesting Romney's charge was "unhinged."
At a campaign stop in Chillicothe, Ohio, Romney said Obama has "pushed Republicans and Democrats as far apart as they can go" and accused the president and Democrats of pursuing a campaign strategy intended to "smash America apart."
"If an American president wins that way, we all lose," Romney said.
"So, Mr. President, take your campaign of division and anger and hate back to Chicago and let us get about rebuilding and reuniting America," the former Massachusetts governor said.
"Governor Romney's comments tonight seemed unhinged, and particularly strange coming at a time when he's pouring tens of millions of dollars into negative ads that are demonstrably false," Obama campaign press secretary Ben LaBolt said in an e-mail to the liberal Talking Points Memo Web site.
Earlier in the day, Romney told a crowd of miners at a coal mine in Beallsville Vice President Joe Biden "said coal is more dangerous than terrorists. Can you imagine that? This tells you precisely what he actually feels and what he's done and his policies over the last 3 1/2 years have put in place the very vision he had when he was running for office."
Romney contended Obama was running ads in Ohio saying he supports coal while telling people in other states only wind and solar power are needed.
Politico said the White House and Obama's campaign have spent months working to counter Republican claims the president has "declared war on coal." Obama's Ohio radio ad touts the administration's support for "clean coal," and slams Romney for denouncing a Massachusetts coal-fired power plant in 2003.
While Romney campaigned in Ohio, the president was on a campaign bus in Iowa for the second day.
Romney's visit to the coal mine came on the last day of his four-state bus tour that includes two more events in Ohio.