"I strongly support this bill, and I encourage the Congress to pass it and send it to me for my signature, so stem cell science can progress, without ethical and cultural conflict," Bush said.
Shortly after taking office in 2001, Bush issued an executive order that permitted for the first time federal funding of human embryonic stem cell research. But he limited it to batches available as of that August.
The bill first passed by the Senate on Wednesday would lift this restriction, but keep in place one that prohibits use of federal funds to create embryos via cloning or other technology.
To override a veto, a two-thirds majority vote would be needed in the Senate and House of Representatives. In January, the House passed a similar bill, but far short of a two-thirds margin.
Yet Republican and Democrat backers predicted such legislation will eventually become law.
"He (Bush) is not going to be president forever," said Sen. Russ Feingold, a Wisconsin Democrat.
Stem cells are a kind of master cell for the body, capable of growing into various tissue and cell types. Scientists hope to use the cells from embryos to repair damaged tissue.
(Additional reporting by Maggie Fox, Richard Cowan and Toby Zakaria)
