WASHINGTON — The House Intelligence Committee unanimously passed a bill on Thursday to replace the National Security Agency’s program that is systematically collecting bulk records about Americans’ phone calls.

The panel decided to abandon its own version of legislation to replace the program and instead embrace a bill developed by the House Judiciary Committee, which passed its measure, called the USA Freedom Act, unanimously on Wednesday.

The two committees share jurisdiction over surveillance matters and had been seen as rivals, with the Intelligence Committee more concerned about preserving expansive surveillance powers and the Judiciary Committee more focused on imposing privacy protections.

But a single N.S.A. reform bill now moves to the floor of the House of Representatives with unanimous and bipartisan backing from both committees with jurisdiction over the matter, giving it added momentum. President Obama has already embraced its rough outlines.