But, after the 63-34 vote failed to achieve the required two-thirds majority to override a presidential veto, a statement from Mr Bush said: "This bill crosses a moral line that I and many others find troubling.
"If it advances all the way through Congress to my desk, I will veto it.''
Exponents of the research say that diseases such as Alzheimer's could be eradicated by stem cell scientists, but critics say that the harvesting of cells from embryos is unethical.
Mr Bush's sole presidential veto in his six years in the White House came in 2006 when he blocked a similar bill from becoming law.
The president has instead given his backing to plans, also approved by the Senate, to fund research where cells are taken from amniotic fluid, placentas and embryos that have died of natural causes.
Speaking before yesterday's vote, Democrat Claire McCaskill urged her fellow senators to "unleash America's scientists".
"Not every day do we have the opportunity to vote to heal the sick," she insisted.
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