Washington (CNN) A group of lawmakers of both parties is putting increasing pressure on House Speaker Paul Ryan to make a commitment to bring immigration legislation to the floor and allow an open debate like the Senate.

In a letter shared first with CNN, the bipartisan Problem Solvers Caucus is writing to Ryan on Wednesday to request that he not only make a clear commitment to call to the floor a bill that would resolve the Deferred Action for Childhood Arrivals program that the President is ending -- they ask that he also commit to an open process that would not tip the scales for one party.

"Specifically, we seek your commitment that the House will debate and vote on all serious and substantive proposals, particularly those offered on a bipartisan basis, as well as any bill approved by the full Senate," wrote Reps. Fred Upton, R-Michigan, and Peter Welch, D-Vermont. "A 'Queen of the Hill' rule should be employed that establishes the proposal receiving the most votes as the position of the House."

The group is made up of 48 members of the House, split evenly by party. Ryan has said he will observe the so-called "Hastert Rule" of not calling any legislation that does not have the support of a majority of Republicans. Some stalled immigration proposals could likely pass the House, but with a majority of Democratic votes and fewer Republican votes.

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