The House speaker, John A. Boehner of Ohio, striking a conciliatory tone a day after the Republican Party’s electoral drubbing, said on Wednesday that he was ready to accept a budget deal that raises federal revenue as long as it is linked to an overhaul of entitlements and a reform of the tax code that closes loopholes, curtails or eliminates deductions and lowers income tax rates.

Mr. Boehner’s gesture was the most explicit offer he has made to avert the “fiscal cliff” in January, when billions of dollars in tax increases and automatic spending cuts go into force. And it came hours after Senator Harry Reid of Nevada, the majority leader, offered his own olive branch, saying “it’s better to dance than to fight.”

“Mr. President, this is your moment,” Mr. Boehner told reporters in the Capitol. “We’re ready to be led, not as Democrats or Republicans, but as Americans.”

The offer may be enough to bring the parties to the table in the wake of an election that kept President Obama in power, strengthened the Democrats’ grip on the Senate and chipped away at the still-large Republican majority in the House.