Adds analyst comment, updates prices; moves dateline to London

LONDON, June 4 (Reuters) - Copper shrugged off an early dip to trade slightly higher on Thursday, as dwindling inventories offset concerns that the prolonged conflict in the Middle East could curb demand growth.

Benchmark three-month copper CMCU3 on the London Metal Exchange was up 0.1% at $13,832 a metric ton at 0930 GMT, inching back towards the $14,000 mark it crossed earlier this week.

The metal, widely used in power, construction and manufacturing, slipped as much as 0.9% earlier in the session on uncertainty over progress in talks to end the Iran war and concerns U.S. interest rates may stay higher for longer.

Prices turned higher after LME data showed orders to withdraw another 23,475 tons of copper from LME warehouses, including 18,975 tons from the U.S. storage hub in New Orleans.

The arbitrage to ship metal from the LME to the U.S. COMEX exchange is wide open, so it makes sense to cancel stock held on the LME, a trader said.

There were another 2,600 tons of copper outflows from LME warehouses - in New Orleans and Kaohsiung - on Wednesday, taking inventories MCUSTX-TOTAL down to 379,975 tons, the lowest since April 2.

ING analyst Ewa Manthey said copper prices had eased from recent highs as rising U.S.-Iran tensions could weigh on the demand outlook.

"The move is being driven by a combination of weaker growth expectations, higher energy costs and profit-taking after a tariff-driven rally," she added, referring to the prospect of the U.S. imposing a duty on refined copper imports.

The U.S. Department of Commerce is due to make a recommendation to President Donald Trump on copper tariffs by the end of the month.

The rest of the LME complex was trading lower. Aluminium CMAL3 dipped 0.7% to $3,678.50, tin CMSN3 shed 1.9% to $56,305, zinc CMZN3 slid 1% to $3,575, lead CMPB3 lost 0.5% to $2,012.50 and nickel CMNI3 fell 1.2% to $18,635, touching its lowest since May 19.