WASHINGTON—The White House issued a rare veto threat in response to a bipartisan Senate bill that would slap Iran with new sanctions if it violates an interim deal reached last month to curb its nuclear program.

The threat sets up a standoff in the new year between President Barack Obama and more than two dozen Senate Democrats and Republicans who introduced the legislation on Thursday. The challenge to Mr. Obama is particularly stark because half of the lawmakers sponsoring the new bill are from his own party.

The bill could also imperil Mr. Obama's efforts to reach a diplomatic end to the decadelong standoff over Iran's nuclear program, which administration officials hope will be a signature achievement of his second term.

Iranian officials have repeatedly threatened in recent days to back out of negotiations with the U.S. and other global powers over Tehran's nuclear program if Washington enacts new sanctions.

White House Press Secretary Jay Carney criticized the Senate move, saying such sanctions would undermine Mr. Obama's diplomatic efforts "no matter how they're structured."