* Brent premium to WTI widens to more than $8/bbl
* U.S. jobless claims lower than expected
* Heating oil, RBOB futures rise slightly
* U.S. crude oil inventories hit record high (Adds trading volumes, updates late prices)
NEW YORK, May 9 (Reuters) - Brent crude edged up in volatile trade on Thursday, and U.S. crude settled slightly down, as investors weighed Middle East tensions against weak demand and high inventories.
Brent crude for June rallied just before the close of the trading session to end 13 cents higher at $104.47 per barrel, up more than $1 from a session low of $103.45. It subsequently fell in post-settlement trading and was down 11 cents at $104.23 at 4:47 p.m. EDT (2047 GMT).
U.S. oil fell 23 cents to settle at $96.39 a barrel, after touching a low of $95.35 in intraday trading. It was down 72 cents to $95.90 in post-settlement trading.
The relatively narrow trading range suggested prices were firming.
"Today's trade feature largely represented consolidation with (U.S. crude) and Brent," Jim Ritterbusch, president of Ritterbusch and Associates, said in a research note.
Analysts said data released on Wednesday by the U.S. government showing domestic stockpiles of crude had hit another record last week due to growing production weighed on markets early.
On Thursday, the U.S. Labor Department reported that the number of Americans filing new claims for unemployment benefits dropped last week to the lowest in nearly 5-1/2 years.
U.S. equity markets slipped, coming off record highs, while the dollar rose against the yen and the euro.
Oil traders said the absence of support from geopolitical tension or bullish equity markets meant taking a closer look at weak supply-and-demand fundamentals.
"There's a tug of war here; the demand is not going to be there, but the economy is slowly improving." Mark Waggoner, president at Excel Futures in Bend, Oregon.
Brent has slipped from a one-month high of $105.94 on Tuesday, when Israeli air strikes on Syria stoked supply fears.
Thursday's U.S. crude trading was inside Wednesday's range, indicating price consolidation. Brent dipped slightly below Wednesday's low but remained largely in a range of just over $1.
"There's too much crude oil production in the world, and when traders become worried about that, they end up selling," said Tim Evans, energy specialist at Citi Futures Perspective.
"Today we have an example of what the market looks like when the S&P is not setting new records," Evans said.
U.S. crude volumes were 13 percent higher than the 30-day moving average while Brent's were 12 percent below the 30-day moving average.
SPREAD ABOVE $8; CRACK TRADING
Expectations that further capacity utilization could suck more oil out of the U.S. Midwest storage hub over to U.S. refiners narrowed the spread CL-LCO1=R between U.S. crude, also called West Texas Intermediate or WTI, and Brent to a low of $7.47, its narrowest since January 2011.
It later widened back to close just above $8, a narrowing of nearly $6 since the beginning of April when it closed at $14.01.
Ritterbusch cited "an accelerated supply drain out of Cushing," the U.S. hub for crude oil, as behind most of the spread's contraction, as well as ample supply in Europe which would weigh on Brent prices.
Heating oil and RBOB gasoline rose slightly, indicating traders may be exploiting the crack spread - the differential between crude oil prices and the products derived from "cracking" open crude by refining it, analysts said.
"Products up, while the crudes are down has the look of crack spread buying," said John Kilduff, partner at Again Capital LLC in New York. (Additional reporting by Christopher Johnson in London and Manash Goswami in Singapore; Editing by Bob Burgdorfer, Dale Hudson, David Gregorio and Jim Marshall)