* Copper cancelled warrants help boost prices
* Zinc touch 3-month high, nickel touches 4-month high (Updates with closing prices)
By Pratima Desai
LONDON, Jan 31 (Reuters) - Copper prices hit seven-week highs on Thursday as the dollar slipped after the U.S. central bank signalled further interest rate rises could be shelved, but gains were capped by shrinking activity in China's manufacturing sector.
Benchmark copper on the London Metal Exchange ended up 0.5 percent at $6,169 a tonne. Earlier the metal, used widely in power and construction, touched $6,199 a tonne, its highest since Dec. 13.
"Copper will ultimately be driven by economic and industrial production growth in China, where lead indicators like credit growth and capital investment are slowing," said Liberum analyst Richard Knights.
RATES: The Federal Reserve left interest rates unchanged on Wednesday and discarded its promises of "further gradual increases". Fed Chairman Jerome Powell said the case for rate rises had "weakened" in recent weeks.
That weighed on the U.S. currency, which when it falls makes dollar-denominated assets cheaper for holders of other currencies.
CHINA: China's manufacturing sector contracted for the second straight month in January. Even with government efforts to spur activity, concerns are growing that China may be at risk of a sharper-than-expected slowdown if the trade war with the United States drags on.
DEMAND: China accounts for nearly half of global copper consumption estimated at around 24 million tonnes this year.
GROWTH: China's economy grew at the weakest pace in nearly three decades last year due to weak domestic demand and the trade dispute with the United States.
WARRANTS: Copper has also been helped by worries about a tight LME market as cancelled warrants - metal earmarked for delivery from LME registered warehouses - at 44,125 tonnes make up nearly 30 percent of total stocks.
NICKEL: Prices of the stainless steel material were up 1.0 percent at $12,480 a tonne from an earlier three-month high at $12,515 a tonne. Its rise has been fuelled by falling LME stocks and worries about disrupted supply from Brazil's Vale .
But the discount for the cash contract against the three-month CMNI0-3 at nearly $70 a tonne indicates the market is not concerned about nearby supplies.
ZINC: Prices of the metal used to galvanise steel gained 1.2 percent to $2,718 a tonne. Earlier, it touched a seven-month high at $2,737, partly due to concerns about falling supply from China due to an environmental crackdown.
"(A) combination of poor profitability and difficulties in complying with environmental regulations resulted in Chinese smelter production (last year) falling to its lowest level since 2013," Wood Mackenzie analysts said in a note.
PRICES: Aluminium was little changed at $1,910 a tonne, lead climbed 1.0 percent to $2,112 and tin rose 0.2 percent to $20,850 a tonne.
Reporting by Pratima Desai; Editing by Mark Potter and David Evans