Before the vote, Democrats argued in vain for minority Republicans to break with Bush and support taking up the measure.
The senate's rare Saturday session came on a day when Condoleezza Rice, the US secretary of state, made an unannounced visit to Baghdad.
Carl Levin, a Democratic senator and chairman of the body's Armed Services Committee, said: "If we believe plunging into Baghdad neighbourhoods with more American troops will not increase chances of success, we are duty bound to say so, and a minority of senators should not thwart that expression".
The senate Republican leader, Mitch McConnell, had called for the vote to be defeated, accusing the Democrats of "chicanery".
"We will not be forced to vote for a resolution that says we support the troops but does not ask us to seal that pledge with a promise to help them carry out that mission in the only way they can - funding their mission."
The House of Representatives defied Bush on Friday by voting 246 to 182 against the troop increase in what amounted to the first such rebuke since the US-led invasion in March 2003.
The House measure passed with support of virtually all the chamber's 233 Democrats and 17 of its 201 Republicans, many worried about their political fate if they stick with the president on the war.
Polls say most Americans oppose sending more troops to Iraq.
But in the senate, procedural rules allow a minority to block debate and Democrats have a small 51-49 majority.
The upper chamber has been deadlocked on the issue since February 5 when an attempt to bring up a similar resolution opposing the troop increase failed.