Asia Pacific markets traded cautiously on Tuesday, following the previous day's rally, as new doubts emerged overnight about the partial U.S.-China trade deal.

In South Korea, the Kospi index closed fractionally higher at 2,068.17. Japan's Nikkei 225 jumped 1.87% to 22,207.21 and the Topix index added 1.56% to 1,620.20 after Japanese markets were closed Monday for a public holiday.

Chinese mainland markets fell: The Shanghai composite slipped 0.56% to 2,991.05, the Shenzhen composite declined 1.1% to 1,641.94 and the Shenzhen component was down 1.17% to 9,671.73.

Pork prices in China jumped around 69% on-year in September due to ongoing shortage of the meat following an outbreak of African swine fever. Overall, the consumer price index was said to have increased 3% on-year last month while the producer price index fell by 1.2%.

Hong Kong's Hang Seng index declined 0.11% in late-afternoon trade.

Australia's ASX 200 wavered between fractional gains and losses to close up 0.14% at 6,652.The heavily weighted financial subindex reversed declines to trade up 0.29% while the energy sector fell 0.85% and materials was down 1%.

Overnight, stocks closed slightly lower on Wall Street and declined in major European markets.

"We have started the new week in a more cautious mood with the US-China trade vibes now starting to show some signs of friction," Rodrigo Catril, senior foreign-exchange strategist at the National Australia Bank, wrote in a morning note. "China wants more talk time to iron out details and it also wants the tariff stick to go away, but overnight comments from Treasury Secretary Steven Mnuchin suggests otherwise."