Officials provided no details of the conversation between Obama and Boehner, which came on the same day the president, hewing to a hard line, publicly warned congressional Republicans not to inject the threat of a government default into the already-complex issue.
"It's not a game I will play," Obama told a group of business leaders as Republicans struggled to find their footing in talks with a recently reelected president and unified congressional Democrats.
Among the Republicans, Sen. Tom Coburn of Oklahoma became the latest to break ranks and say he could support Obama's demand for an increase in tax rates at upper incomes as part of a comprehensive plan to cut federal deficits.
Officials said after the talk between Obama and Boehner that there was no immediate plan for a resumption of negotiations to avoid the cliff. At the same time, they said that for the first time in a few days, at least one top presidential aide had been in touch with Republicans by e-mail on the subject.
Each side has been declaring that the crisis can be avoided if the other will give ground.
It has been several days since either the president or congressional Democrats signaled any interest in negotiations that both sides say are essential to a compromise. Presidential aides have even encouraged speculation that Obama is willing to let the economy go over the fiscal cliff if necessary and gamble that the public blames Republicans for any fallout.
Eventually, Democrats acknowledge, there will be compromise talks, possibly quite soon, toward an agreement that raises revenue, reins in Medicare and other government benefit programs, and perhaps raises the government's $16.4 trillion borrowing limit.
For now, the demonstration of presidential inflexibility appears designed to show that, unlike two years ago, Obama will refuse to sign legislation extending top-rate tax cuts and also to allow public and private pressure to build on the Republican leadership.
Treasury Secretary Tim Geithner underscored the president's determination when he told CNBC the administration was "absolutely" prepared to have the economy go over the cliff if its terms aren't met. "The size of the problem is so large that it can't be solved without rates going up," he said.
So far, the GOP has offered to support nonspecified increases to raise tax revenue by $800 billion over a decade but has rejected Obama's demand to let the top income tax rate rise from 35 percent to 39.6 percent.
To buttress their case, Republican officials in Congress pointed to numerous proposals that Obama has previously advanced that could generate the same amount of revenue he is seeking - without raising rates. The list includes limiting the tax deductions taken by upper-income taxpayers, raising taxes on the oil and gas industry, and curbing or eliminating the deductibility of tax-exempt bonds.
Obama delivered his latest warning at the meeting of the Business Roundtable a few blocks from the White House.
He said he was aware of reports that Republicans may be willing to agree to higher tax rates on the wealthy, then seek to extract spending cuts from the White House in exchange for raising the government's borrowing limit.
"That is a bad strategy for America, it's a bad strategy for your businesses and it's not a game that I will play," Obama said, recalling the "catastrophe that happened in August of 2011" - a reference to a partisan standoff that prompted Standard & Poor's to reduce the rating for government bonds.