Three-month copper on the London Metal Exchange declined 1.6 percent to $7,690 a tonne by 0656 GMT, after a gain of 1.4 percent on Friday. Prices ended 1 percent lower last week.
"Europe is the key drag on consumption," said Song Seng Wun, regional economist at CIMB Research Pte in Singapore.
"It's still a cautious demand story, both domestically in China and what's happening in the global markets."
The European Union's leaders agreed after a two-day summit to pursue closer economic ties and stricter budget discipline in the euro zone, but Britain refused to join the pledge.
The dollar strengthened 0.2 percent against a basket of currencies while the euro slipped after the European Union agreement fell short of a convincing plan to deal with the crisis.
The most-traded February copper contract on the Shanghai Futures Exchange slipped 0.3 percent to 56,930 yuan a tonne.
China's copper imports in November reached their highest level since March 2010, rising 17.9 percent on the month to 452,022 tonnes, preliminary data from China's General Administration of Customs showed on Saturday.
The increase in purchases came after prices had fallen, making it cheaper for the world's largest copper user to boost stockpiles.
China produced 448,000 tonnes of refined copper in November, down 4.5 percent on the month, according to data from the National Bureau of Statistics on Friday, with domestic prices also falling.
Concern that China's economic expansion may falter as Europe's debt crisis spreads has driven London copper prices down by 20 percent this year, snapping a sequence of two annual gains.
China's annual economic growth is likely to slow to 8.5 percent in 2012, an academic adviser to the country's central bank said in remarks published on Monday.
Li Daokui, a professor at Tsinghua University, said Beijing could boost spending on basic infrastructure if the government sees any risk of annual economic growth slipping below 8 percent next year, according to a report published on the news portal website.
The latest Reuters poll showed that economists expect China's economy to grow by 8.6 percent in 2012, after an estimated expansion of more than 9 percent this year.
Declines in copper prices may be limited as an Indonesian workers' union plans to extend a three-month strike at Freeport McMoRan Copper & Gold's Grasberg mine until Jan. 15, union official Virgo Solossa told Reuters on Saturday. Grasberg is the world's second-largest copper mine.
Chinese copper smelters aim to convince BHP Billiton, the majority owner of the world's biggest copper mine, to agree to higher treatment and refining charges set by rival Freeport McMoRan for 2012, trading sources said.