WASHINGTON — President Barack Obama and the House speaker, John Boehner, circled each other warily Friday, defending their competing approaches for resolving the budget impasse even as both professed their willingness to reach common ground.

Obama, in his first formal remarks since the night of his re-election, said he would open discussions with congressional leaders next week to seek a compromise, and then, before an applauding crowd of supporters in the White House’s East Room, defended the “detailed plan” that he campaigned on — including higher taxes on the wealthy.

“I’m not wedded to every detail of my plan. I am open to compromise. I am open to new ideas,” he said. “But I refuse to accept any approach that isn’t balanced.

“We have to combine spending cuts with revenue, and that means asking the wealthiest Americans to pay a little more in taxes,” he said, calling for Congress to immediately extend existing tax rates for 98 percent of taxpayers.

Boehner, citing a “cordial” conversation with the president on the morning after the election, said that he was “hopeful that productive conversations can begin soon so that we can forge an agreement that can pass the Congress.”

But he insisted, as the Republicans put it throughout the campaign, that “the problem with raising tax rates on the wealthiest Americans is that more than half of them are small-business owners.” He added, “Raising tax rates will slow down our ability to create the jobs that everyone says they want.”

Their dueling appearances seemed almost like a reprise of the debates over tax proposals, which were the sharpest point of division in the presidential election.

Asked if the results of the election had weakened his hand, Boehner said: “There is a Republican majority here in the House. The American people re-elected the Republican majority.”