* Return to full production pledged by end-September
* U.S. to impose more sanctions on Iran
* Cushing oil stocks at lowest since Oct 2018 - EIA (Adds Kuwait oil sector heightens security, updates prices)
SINGAPORE, Sept 19 (Reuters) - Oil prices edged higher in Asian trade on Thursday after days of turbulence, with markets soothed by Saudi Arabia's pledge to restore full production by end-September at facilities knocked out in drone and missile attacks last weekend.
Brent crude futures rose 8 cents to $63.68 a barrel by 0507 GMT while U.S. West Texas Intermediate (WTI) crude was up 14 cents to $58.25 a barrel.
The steadying of nerves, after a 14.6% jump in Brent prices on Monday - the contract's biggest one-day percentage gain since at least 1988 - came after Saudi Arabia set out the timeline to full operation, and also said it had managed to restore supplies to customers at levels prior to the attacks by drawing from its oil inventories.
Saudi Arabia, the world's leading oil exporter, has said the crippling attack on its oil sites was "unquestionably sponsored" by bitter regional rival Iran. U.S. President Donald Trump said there were many options short of war with Iran and added that he had ordered the U.S. Treasury to "substantially increase sanctions" on Tehran. Iran has denied involvement in the strikes.
"Prices may have found equilibrium for now," said Michael McCarthy, chief markets analyst at CMC Markets in Sydney. Quick recovery in Saudi oil production would confirm disruption could be temporary, he said.
Oil analytics firm Kayrros estimated Saudi Arabia lost about 3.4 million barrels per day (bpd) of oil output after crude oil inventories plunged nearly 10 million barrels as of Sept. 16 compared with pre-attack levels.
Still, the head of the International Energy Agency said on Wednesday it does not see a need to release emergency oil stocks as markets are well supplied.
While tensions in the Middle East remained elevated, the White House's response on Wednesday to Saudi producing evidence that it said implicated Iran in the attacks pointed to a more measured approach in handling the region's issues, said McCarthy at CMC Markets.
Following the attacks in Saudi Arabia, Kuwait's oil sector is on high alert and has raised its security to the highest level as a precautionary measure, a Kuwaiti oil official said on Wednesday.
Separately, weekly data from the Energy Information Administration on U.S. oil inventories provided a mixed snapshot.
Crude oil stockpiles at the world's largest oil producer rose by 1.1 million barrels last week against analysts' expectations for a drop of 2.5 million barrels.
However, stocks in Cushing, Oklahoma, the delivery point for benchmark futures, fell to the lowest since October 2018.
(Reporting by Florence Tan Editing by Kenneth Maxwell & Shri Navaratnam)