WASHINGTON — The House will vote Friday on two measures that are strongly critical of President Obama’s decision to maintain an American role in NATO operations in Libya, reflecting increasing disenchantment among elements of both parties about the United States’ involvement in the conflict.

The decision to put the resolutions to a vote came after Republican leaders earlier this week postponed consideration of one of them, which would direct the president to end American’s military involvement in the operations. It was sponsored by Representative Dennis J. Kucinich, the Ohio Democrat who is one of the most liberal members of the House.

The leadership feared that the Kucinich measure would pass with backing from an unlikely coalition of liberals and conservatives, a step they contended would send the wrong message to allies engaged in other conflicts with the United States.

On Thursday, Speaker John A. Boehner took the unusual step of presenting his own resolution to his caucus to be voted on by the full House on Friday, along with the Kucinich measure.