WASHINGTON — President Barack Obama challenged congressional Republicans on Wednesday to let taxes rise on the wealthiest Americans on both economic and political grounds, noting he campaigned successfully for re-election on the point and contending it would instantly ease the threat of the “fiscal cliff” plunging the nation back into recession.

“A modest tax increase on the wealthy is not going to break their backs,” Obama said of the nation’s top income earners. “They’ll still be wealthy,” he said at his first news conference since winning a second term.

At the same time, the president stressed he was amenable to compromise on other approaches from Republicans who say they will refuse to raise tax rates. “I believe this is solvable,” he said during the news conference.

Asked if it would be a deal-breaker for Republicans to refuse to allow the top tax rate to revert to 39.6 percent from the current 35 percent, he sidestepped. “I just want to emphasize I am open to new ideas if the Republican counterparts or some Democrats have a great idea for us to raise revenue, maintain progressivity, make sure the middle class isn’t getting hit, reduce our deficit.”

Wall Street wasn’t encouraged that agreement was becoming more likely. The Dow Jones industrial average dropped 185 points for the day.

The president’s remarks were his first extended public discussion of the issue that is dominating the postelection session of Congress, and they followed statements earlier in the week from House Speaker John Boehner, R-Ohio, and Mitch McConnell of Kentucky, the Senate GOP leader.

Both men have said they, too, want a compromise and have said they are willing to support additional tax revenues as part of a deal that includes tax reform and measures to recast the government’s largest benefit programs. But they appear to rule out any legislation that raises tax rates.

Boehner arranged a rebuttal news conference for late in the afternoon.

McConnell issued a statement calling on Obama to “propose a specific plan that includes meaningful entitlement reforms to strengthen and protect these programs for future generations.” He referred to Medicare, Medicaid and Social Security.

The president has moved aggressively this week to lay down markers for any negotiations, first meeting with labor leaders and representatives of liberal groups at the White House, then welcoming a delegation of corporate chief executives for a private session moments after wrapping up his news conference.

Aides said the president is prepared to go to the public in the coming days to enlist support for his position. He said Wednesday, “The American people understood what they were getting” when they voted for him after a campaign that focused heavily on taxes.

Obama is expected to welcome the top leaders of both political parties to the White House on Friday for their first postelection face-to-face discussion of the fiscal cliff, the combination of tax increases and across-the-board spending cuts that will take effect as 2012 gives way to the new year unless Congress intervenes.

Economists in both parties have cautioned that, given the sluggish state of the economy, a return to recession is likely unless lawmakers and the president reach a compromise on legislation.

At his news conference, Obama laid out bleak prospects if he and lawmakers can’t reach agreement.

“Everybody’s taxes will automatically go up, including the 98 percent of Americans who make less than $250,000 a year, and the 97 percent of small businesses who earn less than $250,000 a year. ... Our economy can’t afford that right now,” he said.

As an alternative, the president suggested that Congress pass legislation immediately to “prevent any tax hike whatsoever on the first $250,000 of everybody’s income,” a measure that he noted has passed the Senate and that Democrats in the House are ready to embrace.

“We should not hold the middle class hostage while we debate tax cuts for the wealthy, and we should at least do what we agree on, and that’s keep middle class taxes low,” he said.

He said enactment of legislation along those lines would eliminate half of the fiscal cliff, and he suggested that he and lawmakers could then “shape a process whereby we look at tax reform” and “take a serious look at how we reform our entitlements, because health care costs continue to be the biggest driver of our deficits.

Obama signed legislation two years ago extending the Bush-era tax cuts in their entirety after saying he wouldn’t.

Asked why this time will be different, he said, “What I said at the time was what I meant, which is that this was a one-time proposition.”

Now, he said, legislation that keeps most of the cuts in place but not those for the upper-income earners would be “actually removing half the fiscal cliff.”

White House Press Secretary Jay Carney said the president would bring to the table a proposal for $1.6 trillion in new taxes on business and the wealthy when he begins discussions with congressional Republicans, a figure that Obama outlined in his most recent budget plan. The targeted revenue is twice the amount Obama discussed with Republican leaders during debt talks during the summer of 2011.

Carney said the figure, combined with $1.1 trillion in spending cuts already signed into law, would reduce deficits by $4 trillion.