The most-active rubber contract on the Shanghai futures exchange for January delivery fell 75 yuan ($10.52), or 0.6%, to 11,730 yuan per tonne.
China's new technically specified rubber (TSR) 20 futures contract fell 0.7% to 9,980 yuan per tonne.
TOCOM's TSR 20 futures contract for February delivery were unchanged at 148.9 yen per kg.
The front-month rubber contract on Singapore's SICOM exchange for October delivery last traded at 129.80 US cents per kg.
US President Donald Trump said on Wednesday a deal to end a nearly 15-month trade war with China could happen sooner than people think and that the Chinese were making big agricultural purchases from the United States, including of beef and pork. The US dollar was quoted around 107.64 yen on Thursday, versus 107.76 on Wednesday.
Oil prices edged lower on Thursday, extending losses from the previous two sessions, as Saudi Arabia quickly regained production volumes after an attack on its oil facilities and amid increasing signs of slowing demand.
Japan's benchmark Nikkei stock average was last slightly up 0.1%.