(Corrects dates of next meetings, paragraphs 9 and 18)

PITTSBURGH - The Group of 20 rich and developing economies, fresh from a triumphant show of unity at Pittsburgh, faces months of deal-making and communication to markets that will test its credibility as the premier global forum for economic cooperation.

It worked, G20 leaders declared on Friday of their response to the global financial crisis. Our forceful response helped stop the dangerous, sharp decline in global activity and stabilize financial markets, they said in the final summit communique.

The summit host, U.S. President Barack Obama, called the gathering a success for a commitment to global economic growth that is balanced and sustained and cited in particular a deal to phase out fossil fuel subsidies.

I am proud that the G20 nations agreed to phase out $300 billion worth of fossil fuel subsidies. This will increase our energy security, reduce greenhouse gas emissions, combat the threat of climate change, and help create the new jobs and industries of the future, he said on Saturday in his weekly radio and Web address.

The leaders agreed that their summits would supplant those of the Group of Seven nations as the high table of global policy making, promising to give rising powers such as China more say in rebuilding and guiding the world economy.

While G7 states were right to accept the inevitable dilution of global economic power caused by the rapid industrialization of poorer countries, analysts said the size and diversity of the group would probably complicate policy coordination.

There are a lot of cooks in the kitchen ... I would wait until we declare victory, said Simon Johnson, a former chief economist of the International Monetary Fund. They have to prove their value and legitimacy.

Challenges to the group's new mantle lie everywhere, from inertia on climate change to skepticism in global financial markets.

G20 nations will remain in the spotlight at the IMF meetings in Istanbul next month, a G20 finance ministers meeting in Scotland in November and the U.N. climate change talks in December.

DISAGREEMENT

Markets were unlikely to react to the support in Pittsburgh for a U.S.-led push to reshape the global economy by smoothing out huge surpluses in exporting powerhouses such as China and large deficits in big importers such as the United States.

Any indication of unity will move the dollar, Christopher Low, chief economist, FTN Financial in New York. But disagreement will rule and that should result in no market reaction.

G20 leaders agreed to work together to assess how domestic policies mesh and to evaluate whether they were collectively consistent with more sustainable and balanced growth.

Countries with sustained, significant surpluses -- a description that fits China -- pledged to strengthen domestic sources of growth, according to the communique. By the same token, countries with big deficits -- such as the United States -- pledged to support private savings.

The leaders agreed to shift some voting rights at the IMF to under-represented countries such as China from rich ones, another sign of the changing balance of economic power accelerated by the financial crisis.

The leaders pledged to keep emergency economic support in place until sustainable recovery was assured, an increasingly sensitive issue for global financial markets.

On Friday the MSCI world equity index hit a 1-week low, with some investors saying they were preparing for an eventual rise in borrowing costs.

There's real uncertainty coming into the policy setting. And this is making it harder work for the rally to be sustained, said Michael Dicks, head of research and investment strategy at Barclays Wealth.

The next G20 summit will in June in Canada. The meeting after that will be in November 2010 in South Korea, where the central bank is poised to become the first in the group to raise interest rates since the collapse of Lehman Brothers a year ago threatened to rupture the global financial system.

SLOW PROGRESS

Despite the show of solidarity, there were some sources of friction. Many Europeans were frustrated that little was agreed on how to pay for fighting climate change, particularly with a December climate summit in Copenhagen fast approaching.

I do not hide my concern at the slow rate of progress ... It's time to get serious now, not later, European Commission President Jose Manuel Barroso said in a statement.

The leaders agreed that firms should be able to claw back or reclaim pay and bonuses in certain instances. The measure was aimed at making sure bankers don't get huge payouts for making risky bets that later go bad.

They are accomplishing all sorts of small things like pay guidelines on bank executives, said Low of FTN Financial.

On the really important things like increasing bank capital limits and limiting carbon emissions, we are just too far apart.

(Reporting by Reuters G20 team; Additional reporting by Richard Leong in New York and Natsuko Waki in London; Writing by Dayan Candappa in Singapore; Editing by Jackie Frank)