House Speaker John A. Boehner said Wednesday that Republicans are “willing to accept new revenue” coming to the federal government as part of a new debt deal, offering an early olive branch in the aftermath of Tuesday’s election.

But the Ohio Republican said new tax money must not come from higher tax rates — something President Obama has pushed for, at least for the wealthy — and said it should come instead from getting rid of loopholes that distort the tax code.

“Does the increased revenue come from government taking a larger share of what the American people earn through higher tax rates?” Mr. Boehner told reporters in a speech at the Capitol a day after he saw voters renew but slim his majority. “Or does it come as the byproduct of a growing economy, energized by a simpler, cleaner, fairer tax code, with fewer loopholes, and lower rates for all?”

Agreeing to any new revenue puts Mr. Boehner at odds with some in his own party who have said the government already takes in too much in taxes, and should instead focus exclusively on cutting spending.

Mr. Boehner also signaled that any deal that brings in new money to the government would have to include changes to entitlement programs such as Medicare and Medicaid, which take up an ever-increasing share of government spending.

Mr. Obama ran for re-election on a call to raise income tax rates on Americans with the highest incomes, while holding rates low for everyone else. Republicans, though, said raising taxes on the wealthy amounted to a tax increase on small businesses.

Mr. Boehner pointed back to discussions he had with Mr. Obama last year, during the height of the debt showdown, when he said they talked about a deal that would lower tax rates but close enough loopholes to bring in more money to federal coffers.

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