A fresh row has broken out over Republican presidential challenger Mitt Romney's vow to extend tax cuts for America's richest people after a study found it would likely see the fiscal burden placed on poorer and working class families increase.

Hitting the stump in Ohio, President Barack Obama cited the study – published on Wednesday by Washington thinktank the Brookings Institution – in a speech warning that Romney's plans would simply give extra cash to wealthy people, without stimulating the economy or helping pay off the country's huge deficits.

"He's not asking you to contribute more to pay down the deficit, he's not asking you to pay more to invest in our children's education, or rebuild our roads or put more folks back to work. He's asking you to pay more so that people like him can get a big tax cut," Obama told a crowd in Mansfield, Ohio.

Romney's immense personal wealth, symbolised by his previous use of offshore bank accounts and a refusal to release any more than two years of tax returns, have been rich fodder for Obama campaign negative ads in recent months.

In return, Republicans have accused Democrats of waging "class war" and seeking to demonise successful entrepreneurs.

Romney campaign spokesman Ryan Williams dismissed the report as "liberal", slammed Obama's policies for failing to produce a more impressive economic recovery and said his campaign stuck by its plans for tax cuts.

"It's clear that the only plan President Obama has is more of the same. Mitt Romney believes that lower tax rates and less government will jump-start the economy and create jobs," Williams told the Washington Post.

The campaign also pointed out that one of the report's co-authors – Adam Looney of the Hamilton Project – had served on an economic board advising Obama.

The Brookings report examined what it believes would be the impact of Romney's stated tax reform ideas, such as extending relief for wealthy Americans.

It predicted that the move would cut federal tax revenue by $360bn in 2015 with the cuts predominately favouring upper income taxpayers. It added that taxpayers with incomes over $1m would see after-tax income increase by 8.3%, netting an average tax cut of about $175,000.

Meanwhile the after-tax income of taxpayers earning less than $30,000 would decrease by about 0.9% for an average tax increase of $130. It also added that the huge drop in revenue would be bound to have a social cost.

"Such a reduction by itself would be unprecedented and would require deep reductions in many popular tax benefits ranging from the mortgage interest deduction, the exclusion for employer-provided health insurance, the deduction for charitable contributions and benefits for low- and middle-income families and children," the report's authors wrote.

Looney told The Guardian in an interview that the study had sought to be scrupulously fair and transparent in its projections and predictions. "If you look at the paper we are very explicit about the assumptions that we make. We have bent over backwards to be fair. At the end of the day this is just about basic math," he said.

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