* Iraq exports reach 3.08 million bpd in April
* Dollar strength adds pressure to dollar-denominated oil
* U.S. oil rig count down, but not as much as previous week
* Venezuelan refinery work helps lift products futures (. ..(Updates dollar performance, adds CFTC data, last two paragraphs))
By Robert Gibbons
NEW YORK, May 1 (Reuters) - Oil prices eased off 2015 highs on Friday after Iraq said its crude oil exports hit a record in April, and on pressure from a stronger dollar.
Both Brent and U.S. crude settled well above intraday lows, supported by data showing another slip in drilling rig activity and news of a shut gasoline-making unit in Venezuela.
Venezuela's 645,000 barrel-per-day (bpd) Amuay refinery has halted its catalytic cracking unit for maintenance, helping U.S. RBOB gasoline and ultra-low sulfur diesel (ULSD) futures post higher settlements on the first day of trading with June contracts in front-month position.
June Brent crude fell 32 cents to settle at $66.46 a barrel, after falling to $65.52 and having earlier matched Thursday's 2015 peak of $66.93. Brent jumped 21 percent in April.
U.S. June crude fell 48 cents to settle at $59.15, after hitting a 2015 high of $59.90 and recovering from a $58.32 intraday low. U.S. crude futures gained 25 percent last month.
Trading volume was thinned as some major markets were closed for the May Day holiday.
Friday's pullback was initially sparked by news that Iraq's oil exports rose in April to a record 3.08 million bpd from 2.98 million bpd in March, which served as a reminder of ample supply in the market.
OPEC supply in April rose to its highest in more than two years at 31.04 million bpd, according to a Reuters survey.
"What is driving prices these days is less physical markets, which remain very weak, but more expectations of future tightening," said Amrita Sen, chief oil analyst at Energy Aspects.
Despite a sharp drop in U.S. shale drilling in recent months, there have been few signs that a global supply glut is easing.
Oil services firm Baker Hughes Inc said on Friday that U.S. drilling activity fell by 24 rigs, fewer than the 31 rigs idled last week.
"If markets don't tighten as quickly as people are expecting, the sell-off can be large," Sen said.
The U.S. dollar index posted its best daily gain in a month, up from a two-month low on signs that the U.S. economy may be stabilizing after a soft patch.
The stronger dollar helped pressure several dollar-denominated commodities, including oil.
Speculators cut their net long U.S. crude futures and options positions in the week to April 28, the Commodity Futures Trading Commission said on Friday. (Additional reporting by Ron Bousso in London and Aaron Sheldrick in Tokyo; Editing by David Evans, Bernadette Baum, Richard Chang, Andrew Hay and Ted Botha)