* Trump says trade deal with China could come soon
* U.S. and Japan sign limited trade deal
* Saudi move to restore production adds to supply (Updates prices, adds analyst comment)
LONDON, Sept 26 (Reuters) - Oil steadied on Thursday amid optimism that the United States and China could resolve their trade dispute, though prices came under pressure from Saudi Arabia's moves to restore output quickly after attacks on its oil installations.
Brent crude futures were down 12 cents, or 0.2%, at $62.27 a barrel by 1057 GMT.
U.S. West Texas Intermediate (WTI) crude futures were little changed, losing 3 cents to $56.46 a barrel.
U.S. President Donald Trump on Wednesday signaled that a resolution to the dispute with China might be near, which could eventually boost fuel demand.
A day after delivering a stinging rebuke to China over its trade policies, Trump said Beijing wants to make a deal and it "could happen sooner than you think."
Trump and Japanese Prime Minister Shinzo Abe also signed a limited trade deal that would open Japanese markets to $7 billion of U.S. products annually.
"With the swift resolution of production outages and resilience of Saudis oil sector, barring a repeat of drone attacks, the oil markets focus will, in our opinion, return to the economy and trade wars," global oil strategist Harry Tchilinguirian told the Reuters Global Oil Forum.
"News on the U.S.-China front was positive yesterday, albeit without materially affecting oil prices."
Brent and WTI fell on Wednesday to their lowest since the Sept. 14 attacks on Saudi Arabia.
Prices were weighed down by a surprise 2.4 million barrel build in U.S. crude inventories last week and a faster than expected recovery of Saudi output after the drone and missile strikes on two of its oil-processing plants.
The world's top oil exporter has restored its production capacity to 11.3 million barrels per day, sources briefed on Saudi Aramco's operations told Reuters.
"The oil market has seemingly returned to business as usual," said Norbert Ruecker, head of economics and next-generation research at Julius Baer.
"Instead of the attack-related fallout including disruption and geopolitical risks, the soft economy and stagnant oil demand are back in focus."
Crude futures were pressured by sluggish economic data in leading European economies and Japan.
A firmer dollar, which registered its sharpest daily gain in three months overnight and held steady in Asian trade, also weighed on oil as it makes dollar-traded fuel imports more costly for countries using other currencies.
(Additional reporting by Roslan Khasawneh in Singapore; Editing by Dale Hudson and David Goodman)