(Adds comment, detail, updates prices) MELBOURNE, June 5 (Reuters) - London copper was steady on Monday, supported as the dollar eased following a disappointing U.S. jobs report, while zinc and nickel prices tracked renewed weakness in steel markets. "We think copper should hold its own in June, as the Grasberg strike provides support ... (and) falling stock levels on both the LME and Shanghai should also help," INTL FC Stone said in a report. Freeport McMoRan Inc said last month that mining and milling rates at its Grasberg copper mine in Indonesia had been affected by an extended strike. "Concern about moderating demand trends in China including a slowdown in real estate price growth have unnerved the market," INTL FC Stone added. It sees copper trading between $5,520 and $5,825 this month.
* LME COPPER: London copper was trading flat at $5,665 a tonne by 0607 GMT, following a 0.6-percent loss on Friday. Prices have been trapped in a $5,460-$5,770 range since early May.
* SHFE COPPER: ShFE copper slipped 0.2 percent to 45,290 yuan ($6,657) a tonne.
* LME zinc traded almost three times the volume of LME copper, with traders looking for opportunities in the price gap between London and Shanghai. Chinese prices for the metal, used to galvanize steel, slipped by 1.1 percent, tracking a 2.9-percent fall in ShFE rebar.
* The World Bank on Sunday maintained its forecast that global growth will improve to 2.7 percent this year, citing a pickup in manufacturing and trade, improved market confidence and a recovery in commodity prices.
* Activity in China's services sector expanded at the fastest pace in four months in May thanks to a surge in new orders, a private business survey showed, helping to offset worries about unexpected weakness in manufacturing.
* China agreed to delay an 8 percent quota for electric and hybrid vehicles by a year until 2019, an auto industry source said on Friday, in a major concession for German carmakers seeking to expand in the world's largest auto market. Electric cars are a major growing demand segment for copper.
* Hedge funds and money managers trimmed their net long position in COMEX copper, U.S. Commodity Futures Trading Commission data showed on Friday.
* COMING UP: Euro zone Markit Comp, Services PMI for May at 0800 GMT; US Durable Goods Factory Orders for April at 1400 GMT.
BASE METALS PRICES 0609 GMT Three month LME copper 5661.5 Most active ShFE copper 45270 Three month LME aluminum 1921.5 Most active ShFE aluminum 13730 Three month LME zinc 2532.5 Most active ShFE zinc 21500 Three month LME lead 2111 Most active ShFE lead 16485 Three month LME nickel 8920 Most active ShFE nickel 73460 Three month LME tin 20220 Most active ShFE tin 142520
BASE METALS ARBITRAGE
LME/SHFE COPPER LMESHFCUc3 308.61 LME/SHFE ALUMINIUM LMESHFALc3 -1429.69 LME/SHFE ZINC LMESHFZNc3 431.57 LME/SHFE LEAD LMESHFPBc3 -776.33 LME/SHFE NICKEL LMESHFNIc3 1859.51
($1 = 6.8035 Chinese yuan renminbi)
(Reporting by Melanie Burton; Editing by Joseph Radford)