(Updates prices) HANOI, May 18 (Reuters) - Copper prices rose on Tuesday, as a weaker U.S. dollar made the greenback-priced metals cheaper and more attractive to holders of other currencies, while zinc prices in Shanghai climbed to their highest in more than 13 years on supply concerns in China. Three-month copper on the London Metal Exchange was up 1.2% at $10,497 a tonne by 0704 GMT, while the most-traded June copper contract on the Shanghai Futures Exchange closed up 1.9% at 76,100 yuan ($11,842.51) a tonne. “(It’s) just the overall U.S. dollar weakness,” said a Singapore-based metals trader. The dollar was under pressure on expectations that U.S. interest rates will remain low for an extended period, after Dallas Federal Reserve President Robert Kaplan said he does not expect rates to rise until next year. Meanwhile, Yangshan copper premium SMM-CUYP-CN climbed $1.50 to $38.50 a tonne on Monday, rising for the first time since February and signalling early signs of improved demand for imported metal into China. ShFE zinc jumped as much as 6.1% to its highest since November 2007 at 23,535 yuan a tonne and LME zinc rose as much as 3.1% to $3,108.50 a tonne, its strongest peak since June 2018. “It’s rumoured that some Yunnan-based zinc smelters will cut production due to the shortage of power,” said a China-based analyst. FUNDAMENTALS * Aluminium smelters in Yunnan province were asked to test the feasibility of staggering their power consumption ahead of the ruling Communist Party’s centenary celebrations, according to a document reviewed by Reuters. * The United States and the European Union agreed not to escalate their dispute over U.S. steel and aluminium tariffs, averting steep EU tariff hikes. * LME nickel climbed 1.4% to $18,165 a tonne, SHFE nickel jumped 3.2% to 134,450 yuan a tonne while ShFE lead advanced 2.6% to 15,500 yuan a tonne. * For the top stories in metals and other news, click or $1 = 6.4260 yuan Reporting by Mai Nguyen; editing by Sherry Jacob-Phillips and Jason Neely Our Standards: The Thomson Reuters Trust Principles.