Oil prices rebounded more than $1 on Wednesday as top world oil exporter Saudi Arabia, which has boosted supply to cool prices, said it believed the market had now reached a fair value.

U.S. light crude settled up $1.39 to $37.05 a barrel on the New York Mercantile Exchange (search), while London Brent was up $1.39 to $34.50 a barrel.

U.S. crude has fallen more than $5 from early June's peak at $42.45 a barrel as higher output from the OPEC (search) cartel, especially Saudi Arabia, has helped replenish crude inventories.

Saudi Arabia has been producing 9.1 million barrels per day (bpd) since the start of June, well above its official OPEC production quota.

"I believe the current prices are fair and there is no reason to take any measures either to decrease or increase the production," Saudi Oil Minister Ali al-Naimi told reporters in Riyadh.

Gains accelerated after the U.S. government reported a small 500,000 barrels fall in commercial crude stocks last week. U.S. crude stocks had increased in 17 of the previous 21 weeks and analysts had expected another two million barrel rise.

A big draw in crude stocks in Cushing, Oklahoma, the delivery point for the NYMEX light crude contract, strengthened the report's bullish impact.

Cushing crude stocks fell 1.9 million barrels to 11.8 million barrels, and are down almost 30 percent since registering 16.5 million barrels four weeks ago, the EIA said.

"We had a big draw again in Cushing and that was striking. That makes this report more bullish than the headlines," said Katherine Spector, head of energy research at JP Morgan bank.

Chinese efforts to slow runaway economic growth have helped pull oil prices lower in recent weeks, while in Iraq, this week's handover of power has fed optimism of a slowdown in repeated sabotage attacks that have restricted Iraqi oil exports.

Iraq's infrastructure security chief cautioned on Tuesday that sabotage against the country's oil installations would continue unless neighboring nations cooperate in stopping infiltration of foreigners.

Sabotage attacks on pipelines, which have stopped oil exports several times this year, have kept shipments well below the 2.2 million barrel daily volume before the war.

Analysts warn a major attack on oil facilities could quickly push prices back up again as the higher Saudi supply has reduced the world's spare production capacity.

A move by the Federal Reserve (search) to raise interest rates a quarter percentage point, the first increase in four years, provoked fears of a slowdown in global growth.

"By keeping rates at record lows for such a long time, the Fed encouraged rapid credit growth in both the U.S. and abroad. It is almost inevitable that as rates rise, problems will emerge," said Washington D.C.-based analysts PFC Energy.