"It makes no sense to tell the enemy when you plan to start withdrawing," he said.
The Democratic-led Congress sent Bush the bill on the fourth anniversary of his "Mission Accomplished" speech, during which he declared that major combat operations in Iraq had ended.
The war, however, has dragged on, and has claimed the lives of over 3,300 American soldiers and tens of thousands of Iraqis.
The bill, which would require the Bush administration to start withdrawing U.S. troops from Iraq by Oct. 1, with a goal of ending U.S. combat operations there by next March, was designed to provide nearly 100 billion U.S. dollars for American military operations in Iraq and Afghanistan this year.
Bush said setting a deadline for withdrawal "is setting a date for failure," and that was "a prescription for chaos and confusion."
Urging the Democratic-led Congress to give his troops buildup plan in Iraq "a chance to work," Bush also expressed his desire "to work with the Congress to resolve this matter as quickly as possible."
Bush and congressional leaders from both parties would meet at the White House Wednesday on the spending bill.
He warned that without a war-funding bill, the military "has to take money from some other account or training program so the troops in combat have what they need" and to "consider cutting back on buying new equipment or repairing existing equipment."
Democrats immediately rebutted Bush's veto.
"The president may be content with keeping our troops mired in the middle of an open-ended civil war, but we're not -- and neither are most Americans," said Senate Majority Leader Harry Reid.
Reid said the president's refusal to sign the war spending bill was "his right," but he "has an obligation to explain his plan to responsibly end this war."
"We had hoped that the president would have treated it with respect," House Speaker Nancy Pelosi said.
"Instead, the president vetoed the bill outright, and, frankly, misrepresented what this legislation does," she said.
Acknowledging there was "great distance" between the White House and Congress, Pelosi also expressed the wish to work with Bush to "find common ground" on the war funding bill.
Without sufficient votes in both chambers of Congress to override Bush's veto, Democrats were considering writing a new war spending bill that would provide funding to U.S. troops but also set certain benchmarks for the Iraqi government to meet, news reports said.
Bush announced a reinforcement plan in January by sending over 20,000 additional U.S. troops to Iraq to help quell escalating sectarian violence there, but his plan has met strong resistance from Congress, and the Iraq war, now in its fifth year, has become increasingly unpopular with the U.S. public.
A USA Today/Gallup poll conducted in April found that 57 percent of respondents now felt the Iraq war was a mistake, against 41 percent who said it was not.
In a NBC News/Wall Street Journal poll released last week, 56 percent of those interviewed said they agreed more with the Democrats on a deadline for troop withdrawal, against 37 percent who said they agreed with Bush that there should not be a deadline.
