WASHINGTON (CNN) -- A day after the House passed a bill outlining procedures for interrogating terror suspects and trying them in front of military tribunals, President Bush Thursday urged the Senate to do the same "as soon as possible."

After meeting with GOP Senators, Bush said the bill is "a very vital piece of legislation that will give us the tools necessary to protect the American people."

The bill, which passed the House by a vote of 253-168, is expected to be considered on the Senate floor later in the day. It is a result of a compromise forged last week to ease the concerns of three Republican Senators, John McCain of Arizona, John Warner of Virginia, and Lindsey Graham of South Carolina.

They had objected to the administration's attempt to define the Geneva Conventions' language barring "humiliating treatment and outrages upon personal dignity," arguing that it could open the door for other countries to define their standards of treatment for captured Americans, which could put them in danger. Opponents of the bill say it raises serious legal issues and goes against the recommendations of the U.S. Supreme Court.