* LME/ShFE arb: tmsnrt.rs/2oQ5nm20 (Adds closing prices, update on Grasberg mine)
By Zandi Shabalala
JOHANNESBURG, Aug 29 (Reuters) - Copper rallied to its highest in three years on Tuesday as inventories in London and Shanghai fell and the dollar sank after North Korea raised geopolitical tensions by launching a missile that flew over northern Japan.
Benchmark copper jumped 1.9 percent to close at $6,791.50 tonne. It earlier touched $6,843.50, a level last seen in September 2014.
"The main input to copper is the continued weakness of the dollar which has been particularly aggressive today," said Ole Hansen, a commodities analyst at Saxo Bank, adding that falling stocks had provided underlying support over the last week.
A weaker greenback generally makes dollar-priced metals cheaper for non-U.S. investors, boosting demand.
NORTH KOREA: North Korea sharply escalated geopolitical tensions with the missile launch that drew a sharp reaction from Japanese Prime Minister Shinzo Abe.
LME STOCKS: Inventories in warehouses registered by both the London and Shanghai exchanges showed declines. On-warrant stocks - those not earmarked for removal - in London Metal Exchange (LME) shed 775 tonnes to 112,175 after fresh cancellations.
SHANGHAI STOCKS: Weekly copper stocks in warehouses registered by the Shanghai Futures Exchange declined by 8.2 percent to 187,444 tonnes CU-STX-SGH.
STOCKS: Risky assets such as stocks fell while safe-haven gold jumped over 1 percent as tensions between Washington and Pyongyang grew.
NICKEL: Three-month nickel on the London Metal Exchange ended up 2 percent at $11,710. At one point the contract rose to $11,885, the highest since Nov. 28, 2016.
The metal largely used to make stainless steel is up 18 percent this year in London mainly on the back of supply disruptions and higher steel prices.
"Nickel has supply issues that are still playing out and that's helping, particularly when we see steel prices going up too," said a commodities trader in Sydney.
GRASBERG: Indonesia on Tuesday agreed to let Freeport-McMoRan Inc keep operating its giant Grasberg copper mine, after the U.S. company said it would cede control of its Indonesian unit, ending years of wrangling.
TRUMP DECLINES CHINA PROPOSAL: U.S. President Donald Trump last month rejected a Chinese proposal to cut steel overcapacity, despite the endorsement of some of his top advisers, the Financial Times said, citing people familiar with the matter.
PRICES: Aluminium ended with gains of 1.2 percent to $2,095, lead ended 2.3 percent higher at $2,378, tin inched up 0.1 percent to $20,350, while zinc was 1.5 percent higher at $3,110.
Additional reporting by James Regan in Sydney; Editing by Adrian Croft and Mark Potter