* U.S. gasoline, distillate stocks fall far steeper than expected -API
* Crude oil stocks rise for seventh straight week -API
* Militias fight gun battles in Libyan capital Tripoli
* Iran negotiator says outline nuclear deal possible this week
(Adds comments on Fed tapering, updates prices)
SINGAPORE, Nov 6 (Reuters) - Brent futures rose towards $106 a barrel on Wednesday after investors in Asia latched on to a fall in U.S. oil product inventories, which revived hopes of an improvement in U.S. demand and helped crude recover from a steep fall overnight.
The benchmark also drew support from worries that a prolonged outage in Libya could tighten an already delicate global supply-demand balance at a time of peak winter season demand for heating fuels.
Brent crude gained 57 cents to $105.90 a barrel by 0541 GMT, after settling 90 cents lower at a four-month low in the previous session. U.S. oil rose 50 cents to $93.87, after ending $1.25 down at its lowest in five months.
"We saw big declines in prices overnight. That and data showing a fall in U.S. gasoline and distillate stocks is encouraging people to come and buy back some positions," said Ken Hasegawa, a commodity sales manager at Newedge Japan.
"Overall, trading will remain in a tight range till some of the key economic numbers are out from the United States later this week."
Brent could swing between a low of about $103 a barrel and a high of $109 in the next two weeks, with the U.S. benchmark trading in a range of $92 to $99 a barrel, Hasegawa said.
Data from industry group the American Petroleum Institute (API) showed that gasoline stocks fell 4.3 million barrels, far below analysts' expectations of a 338,000-barrel draw.
Distillate fuel stockpiles, which include diesel and heating oil, fell by 2.73 million barrels compared with expectations of a 1.3 million-barrel drop.
But overall crude inventories rose by 871,000 barrels in the week to Nov. 1 to 382 million barrels, the seventh straight weekly increase.
Investors are now waiting for stockpile data from the U.S. Energy Information Administration (EIA) for clarity on demand.
The turmoil in Libya continued to worry oil investors.
Libyan militia fighters on the government payroll fought each other on the streets of Tripoli in the worst clashes in the capital in weeks, highlighting the government's inability to secure oil fields and ports.
Strikes and armed protests have shut much of the OPEC member's oil output for months.
Yet, continued progress in talks between Iran and the West over Tehran's nuclear programme is taking some of the risk premium away from the market, helping cap the gains in prices.
Iran's top negotiator said that a framework deal on its nuclear programme was possible as early as this week.
Iran resumes negotiations in Geneva on Thursday with six world powers to try to end a stand-off over its programme, which the West suspects may be aimed at developing nuclear weapons, despite Iran's denials.
Gains were also capped by expectations the U.S. Federal Reserve may scale back monetary stimulus later this year, after a report from the Institute for Supply Management (ISM) showed U.S. service-sector business activity picked up. A roll back will boost the dollar, making dollar-denominated assets such as oil more expensive for holders of other currencies.
"The strength in this survey adds to evidence across a raft of business surveys that the shutdown had minimal impact on business conditions," analysts at ANZ said in a note. "The strong US-ISM data led to market speculation that the Fed may taper its asset-purchasing program sooner than expected."
(Reporting by Manash Goswami; Editing by Alan Raybould and Richard Pullin)