AKRON, OHIO — Eager to turn the tables on his rival, President Barack Obama Wednesday cast Republican challenger Mitt Romney as an advocate of tax cuts for the richest people in America at the expense of popular tax breaks for almost everyone else.

Romney, Obama declared, “is asking you to pay more so that people like him can get a big tax cut.”

The president was reprising the middle-class tax debate in Ohio with campaign stops in Republican-friendly Mansfield and in the Democratic stronghold of Akron.

Both sides also rolled out competing new television ads, marking the start of an August drive toward the two parties’ national conventions at month’s end and in early September.

Countering the Republican argument that Obama’s proposals would hurt small businesses, Obama charged that Romney’s tax proposal would force many people to give up popular tax deductions for home mortgages, health care and college tuition.

He pointed to a new report that concluded that Romney’s economic plan would shift the tax burden from wealthy taxpayers to low- and middle-class taxpayers.

“Folks making $3 million or more a year would get a quarter of a million-dollar tax cut,” Obama told more than 2,000 supporters in Mansfield. “But listen, it gets worse. Under my opponent’s tax plan, who do you think gets the bill for these $250,000 tax cuts? You do.”

Invoking the study by economists at the Tax Policy Center and the Brookings Institution, Obama said at both stops that Romney’s plan would result in a tax increase of more than $2,000 a year for an average family with children.

“Ohio, we do not need more tax cuts for folks who are already doing really well,” he said.

The report said Romney’s plan to continue the 2001-03 tax rates and to cut individual and corporate income taxes along with other tax changes would result in $456 billion in lower revenue in 2015. Romney has said his plan would be paid for and would not increase the deficit, but he has not said how he would accomplish that.

The study does not take into account any new spending cuts to make up the lost revenue, but assumes the wealthiest taxpayers would lose tax breaks before middle-income taxpayers.

Because families with children receive significant tax breaks, any changes that reduce those breaks would affect those households more than childless adults, the study concluded.

The Romney campaign said the report is flawed because it does not include reductions in spending and because it does not fully account for potential economic growth caused by lower tax rates.

But the study did account for some economic benefit from the Romney plan, and still concluded that on net, taxpayers making more than $200,000 would see tax cuts and those making less would see tax increases.

Romney’s camp also dismissed the study as partisan, noting that one of its three authors, Adam Looney, was a former member of Obama’s economic policy team. Another author, William Gale, was a senior staff economist for President George H.W. Bush’s Council of Economic Advisers.