WASHINGTON (CNN) -- Three leading senators -- two Democrats and one Republican -- introduced a much-anticipated non-binding resolution Wednesday that explicitly condemns President Bush's plan to increase U.S. troop levels in Iraq.

Sens. Joe Biden, D-Delaware, Carl Levin, D-Michigan, and Chuck Hagel, R-Nebraska, are sponsoring a resolution that states in part, "It is not in the national interest of the United States to deepen its military involvement in Iraq, particularly by escalating U.S. troop presence in Iraq," according to Senate aides.

Biden, a presidential candidate, is the chairman of the Foreign Relations Committee and Hagel is a senior member. Levin is the chairman of the Armed Services Committee.

The bipartisan resolution also says, "The U.S. strategy and presence on the ground in Iraq can only be sustained with the support of the American people and bipartisan support from Congress."

The strategy is to indicate Bush does not have support from the majority of Congress, Senate aides tell CNN.

The resolution also calls on the Iraqi government to take more responsibility for the security of their country and says a political solution is needed to solve Iraq's problems, according to a senior Democratic aide.

Sen. Minority Leader Mitch McConnell of Kentucky has indicated he will try to lead a filibuster against any resolution that condemns the president's new policy in Iraq. But Senate Majority Leader Harry Reid of Nevada has said he believes he has more than the necessary 60 votes to end a filibuster.

Sen. Gordon Smith of Oregon, one of the outspoken GOP critics of the president's policy, told CNN he may not support the resolution because it uses the word "escalation," which Smith claims, "unnecessarily inflames the resolution."