* Asian shares, euro firm as markets cheer Fed rate outlook
* U.S. Fed says no rate hikes until at least late 2014
* U.S. crude inventories rise as imports rebound -EIA
* Coming Up: U.S. weekly jobless claims; 1330 GMT (Updates prices)
By Manash Goswami
SINGAPORE, Jan 26 (Reuters) - Brent crude rose above $110 on Thursday, extending gains on hopes of demand growth revival after the U.S. Federal Reserve said it would keep interest rates low for much longer than previously planned, to help speed economic recovery.
Markets cheered the Fed's rate outlook and Asian shares, base metals, gold and the euro all rose as the comments helped counter concerns among investors about Greece's debt crisis worsening and hurting the global economy. For oil, added support came from worries about supply because of tensions with Iran.
Front-month Brent crude gained 84 cents to $110.65 a barrel by 0717 GMT, reversing two days of losses. U.S. crude gained 70 cents to $100.10, rising for a second day.
"Markets are supported because of concerns about Iran, while the uncertainty over Europe is making it difficult for oil to exit its current trading range," said Ken Hasegawa, a derivatives manager with brokerage Newedge in Tokyo. "For today, the Fed's comments have triggered selling in the dollar, and that has helped oil and commodities across the board to rise."
The dollar index slipped 0.17 percent.
The twin push and pull factors will keep the U.S. benchmark trading in a range between $95 and $104 a barrel, Hasegawa said.
Further optimism about growth in the world's biggest oil consumer came after three major U.S. manufacturers reported better-than-expected quarterly earnings, and as they stuck to their forecasts for this year.
Oil investors are worried that just as the demand outlook looks set to improve, markets face a risk of supply disruption because of tensions between the West and Iran over the Islamic republic's nuclear programme.
The United States has toughened sanctions, while Europe has put in place a move to ban oil imports from Iran.
"The passage of EU sanctions against Iranian crude oil leaves the displaced flows to find a market in Asia before the sanctions take effect in July," analysts at Barclays Capital said in a report. "The mathematics of the potential trades seems to be very delicately balanced, leaving a possibility that not all the displaced crude will find a market easily."
Brent may break a resistance at $110.90 per barrel and rise further to $112.75, while the focus on U.S. oil is whether it will be able to stand firm above a resistance at $100.40 per barrel, which is critical in confirming a double-bottom, according to Reuters technical analyst Wang Tao.
The Fed news also overshadowed data from the Energy Information Administration showing crude inventories rose more than expected as imports rebounded and refinery utilization fell. Stocks increased by 3.6 million barrels in the week to Jan. 20, well over the 800,000 barrel build forecast in a Reuters poll of analysts.
U.S. stockpiles of distillates barrels dropped by 2.5 million barrels, after analysts had forecast no change in inventories for the week. Gasoline inventories dipped by 390,000 barrels, against expectations for a 1.9 million barrel rise.
Yet gains were capped as worries that the European crisis is having an impact on other countries weighed on the market. South Korea's economy grew at its slowest pace since the 2008 financial crisis in the fourth quarter of 2011. Businesses and consumers in Asia's fourth-largest economy have slashed spending in the quarter on concerns that the euro zone crisis could drag advanced economies back into recession.
German Chancellor Angela Merkel deflected pressure to increase the euro zone's rescue fund. International Monetary Fund Managing Director Christine Lagarde called in Berlin this week for the 17-nation currency bloc's financial firewall to be effectively doubled by combining a temporary and a permanent rescue fund to reach 1 trillion euros.
Reporting by Manash Goswami;Editing by Clarence Fernandez