Biden urged the top congressional Republican to spell out his proposals before lawmakers leave Washington for a two-week recess set to start on Thursday.
That followed a missive from McCarthy proposing scaling back domestic spending, clawing back unspent COVID-19 relief funds and other changes that he said would save trillions of dollars.
"My hope is that House Republicans can present the American public with your budget plan before the Congress leaves for Easter recess so that we can have an in-depth conversation when you return," Biden wrote in a letter posted on Twitter.
McCarthy told CNBC earlier that he was prepared to lay out $4 trillion in spending cuts for Biden, if he would agree to meet. Republicans have not yet produced a budget plan of their own and could be weeks or months away from doing so.
McCarthy's proposals, though lacking detail, paralleled the demands of hard-right House Republicans far more closely than ideas put forward by moderate Republicans.
Democrats said Republicans need to first unite behind a proposal.
Biden, a Democrat, has insisted that Republicans who control the House instead raise the $31.4 trillion debt ceiling without conditions and produce a fiscal 2024 spending plan before he will engage in talks about spending.
"Your position - if maintained - could prevent America from meeting its obligations and hold dire ramifications for the entire nation," McCarthy had said earlier on Tuesday.
The political standoff, which has taken hold since Biden and McCarthy held an initial meeting in early February, has raised concerns in the financial markets about a possible U.S. debt default that could cripple the economy.
Republicans have sought to blame Biden, but only Congress has the authority to raise the debt ceiling.
"The only thing missing is a real plan," Democratic Senate Majority Leader Chuck Schumer said in a floor speech.
Members of the hardline House Freedom Caucus said McCarthy's letter paralleled their own spending proposals and claimed it showed adherence to a closed-door agreement with conservatives that allowed him to become speaker in January.
"Today's letter from the speaker to the president represents Speaker McCarthy's fidelity to that agreement," said Representative Matt Gaetz, one of 20 hardliners who forced McCarthy to endure 15 floor votes before being elected speaker.
The House Freedom Caucus has called for cutting nondefense discretionary spending to pre-pandemic levels and allowing it to return only to fiscal 2022 levels after a decade. McCarthy said he wanted to reduce "excessive" nondefense spending to "pre-inflation" levels with limited growth in future years.
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