RUSUTSU, Japan — President Bush and leaders of the world’s richest nations pledged Tuesday to “move toward a low-carbon society” by cutting greenhouse gas emissions in half by 2050, the latest step in a long evolution by a president who for years played down the threat of global warming.

The declaration by the Group of 8 — the United States, Japan, Germany, Britain, France, Italy, Canada and Russia — was the first time that the Bush White House had publicly backed an explicit long-term target for eliminating the gases that scientists have said are warming the planet. But it failed to set a goal for cutting emissions over the next decade, and drew sharp criticism from environmentalists, who called it a missed opportunity.

On Wednesday, leaders of developing nations took up the climate change issue and said that they too supported “a long-term global goal for emission reductions,” but they were not specific and fell short of supporting the Group of 8 declaration.

In a sense, the Group of 8 document represents an environmental quid pro quo. In exchange for agreeing to the “50 by 2050” language, Mr. Bush got what he has sought as his price for joining an international accord: a statement from the rest of the Group of 8 that developing nations like China and India, which have not accepted mandatory caps on carbon emissions, must be included in any climate change treaty.