The House scrapped votes on rival bills late Monday that would narrow the scope of a powerful surveillance tool after an ugly fight broke out among Republicans, likely punting until next year on plans to renew but also limit an expiring wiretapping law at the heart of the program.

In a hastily organized closed-door meeting, Republican members traded accusations and even expletives as they argued over which of two measures to overhaul the law, known as Section 702, should be put to the floor. Under the law, the government can conduct warrantless surveillance of foreigners abroad but also sometimes sweeps in Americans’ private messages.

The dispute effectively upended Speaker Mike Johnson’s plans to have the House vote on both measures this week and send to the Senate whichever one secured a larger majority — a rare move that conservatives vigorously protested.

“I’ve never seen us bring multiple bills at the same time from different committees and put them on the floor and have a beauty pageant,” said Representative Thomas Massie, Republican of Kentucky and a member of the Rules Committee, which would have had to approve the maneuver. “I think this would set a horrible precedent for legislating.”

Lawmakers of both parties are determined to impose limits on the program, which sometimes collects the private messages of Americans in contact with foreign surveillance targets. They are especially at odds over how severely to restrict officials’ ability to plumb Americans’ communications once collected — and Mr. Johnson has not yet endorsed one approach over the other.

On one side, progressive congressional Democrats have joined with harder-right Republican allies of former President Donald J. Trump to rally around a Judiciary Committee bill that would sharply curtail the law while enhancing protections for Americans’ privacy rights.