He said Congress must act against the so-called fiscal cliff, a package of tax rises and spending cuts due early next year.
But in a duelling news conference, Republican House Speaker John Boehner said tax rises would not be acceptable.
Budget analysts warn the US will tip into recession unless a deal is struck.
Mr Obama has repeatedly called for the affluent to pay more, but such a plan is anathema to Republicans.
The fiscal cliff would see the expiry of George W Bush-era tax cuts at the end of 2012, combined with automatic, across-the-board reductions to military and domestic spending.
‘Open to compromise’
In the East Room of the White House on Friday, Mr Obama said: “We can’t just cut our way to prosperity. If we’re serious about reducing the deficit, we have to combine spending cuts with revenue. And that means asking the wealthiest Americans to pay a little more in taxes.”
The Democratic president continued: “I want to be clear. I’m not wedded to every detail of my plan. I’m open to compromise. I’m open to new ideas… but I refuse to accept any approach that isn’t balanced.”
He repeated his oft-stated call for tax rises on earnings over $250,000 (£157,000), while urging Congress to extend existing rates for 98% of taxpayers.
“This was a central question during the election,” said Mr Obama. “It was debated over and over again. On Tuesday night, we found out that the majority of Americans agree with my approach.”
He also invited Democratic and Republican leaders to the White House next week to discuss how to move forward.
A White House spokesman said afterwards the president would veto any bill extending tax cuts for those making more than $250,000.
But battle lines were drawn earlier on Friday, as Speaker Boehner restated his party’s opposition to tax increases.
The most powerful Republican lawmaker told a press briefing that “raising tax rates will slow down our ability to create the jobs that everyone says they want”.
Mr Boehner suggested “special-interest loopholes in the tax code, both corporate and personal” could be eliminated, as he advocated “entitlement reform as well as tax reform with lower rates”.
“Entitlement reform” is Washington-speak for cuts to federal spending – cherished among Mr Obama’s Democratic allies – on programmes such as healthcare for the poor and elderly and Social Security pensions.
Mr Boehner also cited a Congressional Budget Office (CBO) report on Thursday which warned the US economy would fall back into recession if no deal were struck on the fiscal cliff.
The analysis projected that the package of tax rises and spending cuts would cut the ballooning US deficit by $503bn (£315bn) through to next September, but also shrink the economy by 0.5% and cost millions of jobs.
Obama cabinet shake-up
The International Monetary Fund has repeatedly warned that failure by US lawmakers to reach a deal would deepen uncertainty over the global economy.
Investor concerns over the issue have been partly blamed for two straight days of losses on financial markets this week.
Meanwhile, as Mr Obama turns his attention to shaping a second term in office his administration is expected to undergo a shake-up in the coming weeks.
Secretary of State Hillary Clinton, Defence Secretary Leon Panetta and Treasury Secretary Timothy Geithner are among those expected to leave their posts.
Speculation has been swirling in Washington over possible replacements, with Democratic Senator John Kerry among those tipped as a substitute for Mrs Clinton.
Meanwhile, Republicans are carrying out a post-mortem on their presidential election campaign.
Former Secretary of State Condoleezza Rice told CBS News on Friday the party’s loss “really necessitates” new thinking.
They had sent “mixed messages” on immigration and women’s issues, she added.
While Mr Obama carried the popular vote by only a narrow margin, “clearly we are losing important segments” of the electorate, she said.