SINGAPORE, July 27 (Reuters) - London copper prices rose on Monday on hopes that the U.S. Congress would soon agree on a coronavirus relief deal, although gains were capped due to slowing Chinese demand.

Three-month copper on the London Metal Exchange rose 0.5% to $6,446.50 a tonne by 0703 GMT, while the most-traded September copper contract on the Shanghai Futures Exchange tracked overnight losses in London to close 0.4% lower at 51,600 yuan ($7,373.85) a tonne.

U.S. President Donald Trump's top aides agreed in principle with Senate Republicans on a $1-trillion coronavirus relief package, paving the way to negotiate with Democrats.

"This buying (in metals) looks to be related to the U.S. Senate agreeing in principle to the terms of the coronavirus aid bill," said Malcolm Freeman, a director at UK broker Kingdom Futures.

But analysts have warned about weak demand in China.

"Downstream purchase interest remains weak (in China). Copper consumers say weak season has arrived," said an analyst based in China.

Also weighing on prices were U.S.-China tensions and non-materialisation of potential labour strikes in top copper producer Chile.

Antofagasta's avoided a strike at Zaldivar copper mine in Chile, while mediation talks at its Centinela mine were extended in a last-ditch effort to stave off a strike.

FUNDAMENTALS

* OTHER PRICES: LME aluminium rose 0.2% to $1,702.50 a tonne, nickel advanced 0.6% to $13,735 a tonne. ShFE nickel jumped 2% to 110,140 yuan a tonne and tin climbed 2.8% to 146,510 yuan a tonne.

* COPPER: An unprecedented drop in lead demand from the auto battery sector led to massive surpluses, which is only the tip of the iceberg, analysts say.

* ALUMINIUM: China's primary aluminium imports in June rose more than 570% from May.

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($1 = 6.9977 yuan) (Reporting by Mai Nguyen; Editing by Vinay Dwivedi and Uttaresh.V)