President Barack Obama and House Speaker John Boehner signaled Friday a willingness to compromise on tax positions that have led to a budget stalemate, in a bid to defuse partisan tensions before talks next week to avert a year-end fiscal crisis.

Mr. Obama invited Republican and Democratic congressional leaders to the White House next Friday to discuss how to avoid the so-called fiscal cliff, the combination of big tax increases and spending cuts scheduled to begin Jan. 1.

Mr. Obama, in his first statement on the fiscal cliff since winning re-election Tuesday, said any deal must include tax increases on “the wealthy.” He also called on the House to immediately pass a Senate bill that would extend the Bush-era tax cuts on household income under $200,000 a year for individuals and below $250,000 for couples.

Despite his urging for a bipartisan deal, Mr. Obama intends to force Republicans to defend their opposition to Democrats’ bill in the Senate that extends those cuts. He will continue to press his case in coming weeks, administration officials said.

The Bush tax cuts are set to expire Jan. 1. At the same time, $1.2 trillion in automatic spending cuts over 10 years will begin if Congress and the White House don’t act.

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