Senate rejected one resolution, proposed by former presidential candidate Senator John Kerry, calling for combat troops to be withdrawn from Iraq by July 1 next year, by a vote of 86 to 13.
The second bill, calling for troops to begin moving out of Iraq this year but without setting a hard timetable for final withdrawal, was dismissed 60 votes to 39.
The legislation came as amendments to a US Defence Department spending bill were being debated in the Senate.
The Democratic leader in the Senate, Harry Reid, who supported the bill favouring a gradual US troop draw-down, said the United States has to begin reducing its military presence in Iraq.
"I believe it is long past time to change course in Iraq and start to end the President’s open-ended commitment," he said.
"After four long years, more than 2,500 American lives, thousands grievously wounded, hundreds of billions of dollars spent, and threats ignored around the globe, Congress needs to choose a new direction," he said.
Neither bill had been given much chance of passing the Republican-controlled Senate, but lawmakers said they nevertheless reflect the deepening public disaffection with the US military engagement in Iraq.
Republicans welcomed the chance to make the case, just a few months ahead of critical mid-term elections, that they are the party with strong, coherent view on issues related to defence and security.
With the Iraq war increasingly unpopular with the US public, Democrats hope to take control of the Senate or House of Representatives in the November elections.