* iShares Clean Energy ETF, MAC Global Solar Energy Index rise
* Dow Jones U.S. Oil & Gas Index falls before gaining
* Peabody coal down more than 10 percent
* Some investors caution against rushing in to buy "green" stocks (Adds comments, updates prices)
By Sudip Kar-Gupta, Annabella Nielsen and Swetha Gopinath
Dec 14 (Reuters) - A landmark deal to curb global warming dented shares of fossil fuel companies and lifted renewable energy stocks on Monday, although some price swings were muted by the non-binding nature of the pact.
The deal forged at the Paris climate summit is widely seen as the most important climate agreement since the 1997 Kyoto Protocol. It commits rich and poor nations to rein in rising carbon levels and seeks to eliminate net greenhouse gas emissions from human activity this century.
Renewable energy companies are expected to see big upticks in investments to develop new technologies in coming years, while coal and oil companies may see tougher regulations.
"This deal will help boost the mid- to long-term fundamentals in renewable energy generation, especially solar, while making any further investments in fossil fuels increasingly vulnerable," said portfolio manager Thiemo Lang of Zurich's RobecoSAM, which owns solar stocks.
The MAC Global Solar Energy Index was up 4.5 percent. The iShares Global Clean Energy exchange-traded fund , which allows investors to trade a basket of renewable energy stocks, rose 1.4 percent.
The U.S. Oil & Gas Index fell 1 percent before reversing losses, and was up 0.2 percent as oil edged higher after plumbing the lowest levels in about seven years.
Shares of companies that produce coal, seen as dirtier than oil and gas, sank the most. Peabody Energy Corp dropped 12.6 percent, and Consol Energy Inc fell 3.3 percent.
Solar companies welcomed the pact. Their shares have been hammered this year on fears that low oil prices would sap demand for renewable energy, even though the business often relies on government incentives.
"Without question, solar is positioned to make the single biggest contribution of any industry to carbon reduction goals - more than wind, more than efficiency, more than any other technology on the horizon," SunPower Corp Chief Executive Officer Tom Werner said.
Shares of SunPower shot up 8.7 percent $23.40, while First Solar Inc gained 5 percent.
Wind turbine makers, electric car company Tesla Motors , solar panel group SolarEdge Technologies Inc and Albemarle Corp, which supplies lithium for batteries, will benefit from the deal, said Goldman Sachs.
But others cautioned against buying renewable stocks as the Paris agreement is not a binding treaty. It will take effect in 2020 only if it is ratified by more than 55 percent of nations, or nations that cause 55 percent of global emissions.
"I would not just rush in to buy these stocks on the back of the weekend's agreement," said Francois Savary, chief investment officer at investment management firm Prime Partners. "You need to give time to wait for the dust to settle, and 2020 is still a long way out."
Skeptics said the United States, the world's biggest economy, might back away from targets set in the climate agreement if the Republican Party wins the presidential election in November.
Others said there would be plenty of new business in the rest of the world.
"There are a lot of U.S. solar companies and equipment manufacturers that are active globally," said Alex Klein of IHS in Cambridge, Massachusetts. "So for those companies, renewable energy policies and goals created around the world create a lot of opportunities, regardless of the landscape in the U.S." (Additional reporting by Amrutha Gayathri; Sinead Carew and Henrik Stolen; Editing by Terry Wade, Lisa Von Ahn and Meredith Mazzilli)