* U.S. oil crude inventories up, countering expectations
* Poor U.S. economic outlook weighs on demand
* Washington to send envoy to Tehran for talks
SINGAPORE, July 17 (Reuters) - Oil was inching higher on Thursday, following a second consecutive session of steep losses, as a surprise build in U.S. crude oil inventories amid flailing demand continued to weigh on the market.
U.S. crude futures <CLc1> were 40 cents higher at $135.00 a barrel at 0105 GMT, after falling $4.14 to settle at $134.60 a barrel on Wednesday.
The losses, together with Tuesday's drop of $6.44, bring oil close to $13 below last week's all-time peak. London Brent crude <LCOc1> fell $2.56 to $136.19 a barrel.
The slide in prices, which marked the biggest two-day loss in percentage terms since January 2007, propped up stocks on Wall Street, helping it to regain some of the ground lost in recent days on fears over the health of the U.S. banking sector.
"Oil prices are now at a level where you are beginning to see demand adjustments," said David Moore, an analyst at Commonwealth Bank of Australia.
Investors looking to hedge against inflation and the weak dollar have dumped their money into oil and other commodities, contributing to a 50 percent oil price rally this year that reached a peak above $147 a barrel this month.
Dealers said Wednesday's losses were triggered by a 3 million barrel crude stock build in the United States -- in the face of expectations for a decline -- alongside a rise in gasoline and distillate inventories, a report from the U.S. Energy Information administration showed.
"Besides the increase in crude, gasoline, and distillate stocks, it's interesting to note that demand in the United States remains relatively weak as well," Moore said.
The widely watched government report also showed U.S. oil products demand running 2.0 percent below year-ago levels, another sign that soaring prices are cutting into consumer demand for fuel.
Adding to pressure on oil prices, a senior U.S. official said on Tuesday the United States planned to send an envoy to talks this weekend between Iran and major powers over Tehran's nuclear program.
Washington had said previously it would not be involved in any pre-negotiations with Iran unless it gave up nuclear enrichment. The standoff between the Islamic Republic and the West has helped boost oil prices .
Saudi Arabia, the world's top oil exporter, wants to see lower oil prices, Saudi King Abdullah said in an interview with an Italian newspaper.
Oil's six-year rally has also been driven partly by ballooning demand from developing economies such as China and India. (Reporting by Luke Pachymuthu; Editing by Clarence Fernandez)