* State miner produced 385,000 tons in quarter * Codelco battling dwindling ore grades, rising costs * Port strike, lower copper prices weigh on results SANTIAGO, May 30 (Reuters) - Codelco, the world's No. 1 copper producer, said on Thursday its copper output rose around 3 percent in the first quarter to about 385,000 tonnes due to improvements at the Chuquicamata, Radomiro Tomic and El Teniente deposits. The state-owned miner expects record production this year, boosted by its new slice of the coveted Los Bronces deposit and the launch of its Ministro Hales mine, Chief Executive Thomas Keller told Reuters last month. But Codelco, which produces roughly 11 percent of the world's red metal, is battling slumping ore grades in its tired deposits, soaring costs and an uptick in labor unrest as it fights to meet ambitious expansion targets. Codelco has flagged between $500 million and $600 million in minor investments that could be postponed, though this would not affect the miner's mega projects, Chief Financial Officer Ivan Arriagada told reporters. Including Codelco's slice of El Abra and Anglo American's Los Bronces, the miner's first-quarter output jumped roughly 9.4 percent, Arriagada said. Codelco said profits before tax and extraordinary items slumped 43 percent during the January-March period from a year earlier to $867 million, stung by a near Chile-wide port strike and lower copper prices. Codelco had said the extended strike cost it nearly 60,000 tonnes of its copper, equivalent to around $500 million in revenue. Copper prices have fallen 9 percent so far this year on worries over growth in China, the world's top metals consumer. Prices have been pegged for the past month between $7,100 and $7,500 a tonne. In the first three months of the year, direct cash costs skyrocketed 31 percent to $1.70 per pound of copper. Rising prices are a major headache for miners in Chile, the world's No. 1 copper producer.