The Republican-controlled upper chamber failed to endorse the amendment despite a majority of senators backing the proposal in a 49 to 48 vote.
The measure required the backing of two-thirds of the Senate, or 60 votes, for it to be approved and taken forward to a formal vote.
Gay rights groups applauded the amendment's defeat.
Conservative gay rights group, the Log Cabin Republicans, said in a statement that the "Senate gave a resounding defeat to the voices of intolerance who are trying to use the Constitution as a political tool".
The group thanked Republican Senator John McCain and other lawmakers for opposing the measure, in a statement on its website.
"Cynical": Democrats
Mr Bush later said he was disappointed, but thanked the senators who supported the amendment.
The president said the vote marked "the start of a new chapter in this important national debate."
He said it has always taken a number of tries before a constitutional amendment builds the two-thirds support needed in both houses of Congress.
"My position on this issue is clear: marriage is the most fundamental institution of our society, and it should not be redefined by activist judges," he said.
Democrats said the gay-marriage vote was an attempt to muster conservative support before November congressional elections and divert public attention from more pressing issues -- like the war in Iraq -- that reflect poorly on Republicans.
"It is a cynical attempt to score political points by overriding state courts and intruding into individuals' private lives," Democratic Senator Edward Kennedy of Massachusetts said in floor debate before the vote.
He also accused the Republican leadership of asking the Senate to "spend time writing bigotry into the constitution".
He called it "a cynical attempt to score political points by overriding state courts and intruding into individuals' private lives".
Approval slump
Legislative elections are due to be held in November, just five months away, and are expected to be dominated by the war in Iraq, illegal immigration and soaring energy bills.
Many commentators say Mr Bush's push to ban gay marriage is simply a tactic to divert the attention of his conservative support base away from unpopular issues.
The president's approval ratings have slumped dramatically in recent months, and Republicans are trying muster up support to prevent a loss of control of Congress in the November elections.
Forty-five states have passed laws or amended their constitutions to prohibit same-sex marriage, and the 1996 Defence of Marriage Act allows US states to refuse to recognise marriages performed elsewhere.
Several of those bans have been struck down by state judges and court challenges are pending in nine states.
The issue divides US society, but also the highest ranks of the Republican party.
US Vice President Dick Cheney's daughter, who is a lesbian, earlier criticised the amendment as "discrimination".
Mary Cheney, 37, last month told Fox News Sunday that it was "a bad piece of legislation".
"It is writing discrimination into the constitution and, as I say, it is fundamentally wrong," she said.
Conservative Christian groups are opposed to any recognition of gay relationships, and one group, The American Family Association, has boycotted the Ford Motor Company over its support of homosexual groups and advertising in gay publications.
But some gay activists say their relationships have become more accepted across America, pointing to the three Oscar awards won by the gay cowboy love story Brokeback Mountain.