(CNN) The Senate is expected to debate a war powers resolution next week that calls for the United States to end its involvement in the Yemen conflict, but a top Senate Republican leader signaled Thursday GOP leaders would prefer to put off a final vote on the divisive issue until after it can be more closely studied in committee.

"I think it would be better for the committee to consider it and make a recommendation after having a hearing so everybody understands exactly what the consequences are," said Sen. John Cornyn of Texas, the No. 2 GOP leader in the chamber, referring to the Senate Foreign Relations Committee.

The US has provided military support -- including intelligence sharing, logistical support, and mid-flight refueling -- to a coalition led by Saudi Arabia against Iranian-backed Houthis in Yemen . The conflict, which is considered, in part, a proxy war between Saudi Arabia and Iran as they struggle for dominance in the region, has created a dire humanitarian crisis in Yemen.

Three senators -- Mike Lee, a Republican from Utah, Bernie Sanders, an independent from Vermont, and Chris Murphy, a Democrat from Connecticut -- authored the privileged resolution and are working to force a vote on it. They believe the refueling and other actions by the US armed forces are akin to "boots on the ground" and that Congress needs to authorize it.

They described their bill as the "first-ever vote in the Senate to withdraw US armed forces from an unauthorized war."

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