WASHINGTON — Speaker John A. Boehner said Monday that Republicans would insist on trillions of dollars in federal spending cuts in exchange for their support of an increase in the federal debt limit sought by the Obama administration to prevent a government default later this year.

In his most specific statement to date on what Republicans will demand in the debt ceiling fight, Mr. Boehner told the Economic Club of New York that the level of spending reductions should exceed the amount of the increase in borrowing power.

“Without significant spending cuts and changes to the way we spend the American people’s money, there will be no debt limit increase,” Mr. Boehner told members of New York’s business and finance community. “And cuts should be greater than the accompanying increase in debt authority the president is given.” Mr. Boehner said those cuts should be in the trillions of dollars, not billions.

In the speech, delivered ahead of a second round of debt limit negotiations with the White House and Senate Democrats on Tuesday, Mr. Boehner did not provide a timeframe for when the spending reductions would have to be imposed.