The resolution is one of several proposed challenging Bush's war plan but the first offered by such senior Republicans.
In a joint press conference on Monday with Susan Collins and Norm Coleman, fellow Republican senators, Warner said the resolution aimed at registering "genuine concerns" in the Congress about Bush's plan.
Warner's announcement came a day before Bush is to defend his new Iraq strategy in his annual State of the Union speech to Congress.
"Bush's strategy has failed totally in Iraq"
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It also comes as Democrats in the senate, with the support of Chuck Hagel, a Republican, are readying a more strongly-worded, also non-binding resolution that says the troop increase is not in the national interests of the US.
The Democratic resolution heads for debate on Wednesday in the Senate Committee on Foreign Relations.
A spokeswoman for Joe Biden, a Delaware Democrat and chairman of the Senate Foreign Relations Committee, said he was open to working with anyone on the language of resolutions disagreeing with Bush's troop increase.
Warner said: "It is clear that the United States' strategy and operations in Iraq can only be sustained and achieved with support from the American people and with a level of bipartisanship in Congress.
"The purpose of this resolution is not to cut our forces at the current level or to set any timetables for withdrawal but, rather, to express the genuine, and I repeat, the genuine concerns of a number of senators from both parties about the president's plan."
The dropped words used in the first proposal that some senators found objectionable, such as "escalation" to describe the jump in troops, Collins said.
"We've had four other surges since we first went into Iraq," she said. "None of them produced a long-lasting change in the situation on the ground.
"So I am very sceptical that this surge would produce the desired outcome."
'Consider all options'
The non-binding resolution reads: "The Senate disagrees with the plan to augment our forces by 21,500 and urges the president instead to consider all options and alternatives for achieving the strategic goals set forth below with reduced force levels than proposed."
|Warner: Congressional and popular support is|
key to sustaining the US effort in Iraq [AP]
Warner's resolution stresses that it is not aimed at contravening Bush's power as the US commander-in-chief, but insists that congressional and popular support is key to sustaining the US effort in Iraq.
It says the US strategy should focus on conducting counter-terrorism operations in Iraq and training and equipping Iraqi forces to assume security responsibilities.
While Bush's plan also includes those points, its focus is to increase US troop levels in an attempt to re-establish security in Baghdad and Anbar provinces before handing security duties over to the Iraqis.
With already more than 3,000 new troops having arrived in Iraq over the weekend under the new plan - in addition to more than 130,000 already in the country - Bush has remained determined to push ahead with the new approach.
In the House of Representatives, John Boehner, the Republican party leader, said he supports Bush's plan and that his backing is not conditional on the president agreeing to meet the standards that other legislators laid out.
He said he had told the president "that the support is still strong among Republicans, but there are a lot of our members who are sceptical that the plan will work" because of doubts that the Iraqi government will follow through on its commitments.