GOFFSTOWN, N.H. — Borrowing a key element of the anti-government libertarianism that fueled rival Ron Paul’s presidential campaign, Mitt Romney said Monday that he thinks the Federal Reserve should face an audit.

“Very plain and simple, the answer is yes. The Federal Reserve should be accountable. We should see what they’re doing,” Mr. Romney, the presumptive Republican presidential nominee, said at a town hall in New Hampshire.

Mr. Romney also pushed back against President Obama’s claims that the former Massachusetts governor would raise taxes on the middle class if elected.

“Let me tell you the heart of my tax proposal: I will not raise taxes on the American people, I will not raise taxes on middle-income Americans,” Mr. Romney told supporters at St. Anselm College, where he and running mate Rep. Paul Ryan made a grand entrance to the theme song from the movie “Rudy.”

The visit marked the first joint appearance for Mr. Romney and Mr. Ryan in New Hampshire — a state that could prove pivotal come Election Day.

The event gave Mr. Romney a chance to fire back at Mr. Obama, who two days earlier in nearby Windham told voters that Mr. Romney’s tax plan would mean that the wealthy get a tax cut and middle-class families will pay more.

“They have been trying to sell this trickle-down snake oil before,” he said Saturday. “It did not work then. It will not work now.”

Mr. Romney fielded seven questions during the town hall, including the question about auditing the Fed.

Mr. Romney’s answer puts him on the same page of the issue as Mr. Paul, the congressman from Texas who is Mr. Romney’s only remaining active opponent in the GOP presidential race.

Mr. Romney’s embrace of the Paul position puts him at odds with Fed Chairman Ben S. Bernanke, who has said a broad audit would be a “nightmare” for the board.

Earlier this year, the House passed Mr. Paul’s bill to grant the Government Accountability Office the power to conduct such a broad audit, though Senate Democrats have shown no inclination to bring that bill to the floor.

Still, the issue has continued to gain political currency since the 2008 economic collapse.

Mr. Romney said he doesn’t want Congress to meddle too much in the business of the Federal Reserve, which is the independent agency the government set up to manage the country’s monetary policy. But he said it should be audited as part of the effort to make the connections between the government and wealthy campaign contributors more transparent.

Mr. Paul has been lobbying for the Republican platform committee, which was to meet later Monday, to add the Fed audit as an official position.

Virginia Gov. Bob McDonnell, the committee’s chairman, told The Washington Times last month that he supports accountability at the Fed, and said the committee was looking at a number of Mr. Paul’s ideas.

With economic issues at the forefront of the campaign, Mr. Romney and Mr. Obama have been trading attacks over tax policy.

Mr. Obama has cited an independent analysis that says, given the details Mr. Romney has released about lowering tax rates on the wealthy and his pledge not to raise the overall level of taxes, he will have no choice but to eliminate tax breaks that benefit the middle class.

Mr. Obama also argued that Mr. Romney’s push to reshape Medicare into a voucherlike program would force seniors to pony up an additional $6,400 for the same level of benefits — though that figure has been disputed.

Mr. Obama upped the ante further in a surprise visit Monday to the daily White House press briefing, telling reporters that voters “would rightly expect” Mr. Romney to release more of his own personal tax returns.

“I think people want to know that, you know, everybody’s been playing by the same rules including people who are seeking the highest office in the land,” he said, adding his voice to a chorus of Democrats and Republicans who say Mr. Romney, whose personal fortune is estimated as high as $250 million, should be more forthcoming about his tax history.

“If Romney intends to win, he is going to have to make the tax forms public,” the editorial board of New Hampshire’s Union Leader, the state’s largest newspaper, wrote last month. “This storm won’t go away. It will distract from his policy debate with Obama — and it will distract from Obama’s failures, providing the incumbent with the smoke screen he is attempting to create.”

Mr. Romney, though, has said he will not bow to pressure. To date, he has released a tax return from 2010 that showed his effective tax rate was 13.9 percent and a partial return for 2011 that shows he would pay a rate of 15.4 percent.

Last week, his campaign turned down an offer from the Obama campaign to stop talking about his taxes if he would release a total of five years worth of returns.

Mr. Romney said Thursday he has paid at least 13 percent of his income in taxes each year over the past decade.

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