Germany wants a 50% cut in emissions by 2050
He said he would hold meetings bringing together the US and 14 other major emitters, including developing nations, to set targets by the end of 2008.
Mr Bush was speaking ahead of next week's G8 summit, where Germany is expected to call for cuts in emissions.
German Chancellor Angela Merkel welcomed the US proposal, saying it was "common ground" for action.
BBC environment analyst Roger Harrabin says Mr Bush's speech was short on details, and White House aides have made clear Mr Bush will oppose demands for the US to cut emissions and join a global carbon trading system.
The US seems to be trying to set up a separate framework on climate change talks outside the G8, our correspondent says.
Mrs Merkel has called for a major deal, including slowing the rise in average temperatures to 2C this century, by way of a cut in global emissions by 50% below 1990 levels by 2050.
In his speech on Thursday in Washington, Mr Bush said his administration took climate change seriously.
"The United States will work with other nations to establish a new framework on greenhouse gas emissions for when the Kyoto protocol expires," he said.
To achieve this goal, he added, the US would hold a series of meetings bringing together "nations that produced most greenhouse gas emissions, including nations with rapidly growing economies like India and China".
The US has not ratified the Kyoto Protocol, which sets out targets on lowering emissions until 2012.
Mr Bush also repeated that solutions to the problem of global warming would be found through the development of new technologies.
"The United States is in the lead," he said. "The world is on the verge of great breakthroughs that will help us become better stewards of the environment."
The US president urged other nations to eliminate tariffs on clean energy technologies.
British PM Tony Blair hailed the announcement, saying the US was ready to be part of a global climate deal for the first time.
"It's a big step forward and sets the right framework for next week's meeting," Mr Blair said.
But a climate expert with the UK-based environmental group Greenpeace, Charlie Kronick, criticised the plan.
"The only way you can get a grip on carbon emissions is to cap and trade them globally," Mr Kronick told Reuters news agency.
The G8 summit will be held on 6-8 June in Heiligendamm in Germany.