• Asia-Pacific markets traded mixed on Tuesday as major indexes in Japan and South Korea fell.
• Investors remained cautious over rising coronavirus cases, U.S. stimulus negotiations as well as Brexit talks between the U.K. and the European Union.
• The session in Asia follows a mixed overnight session on Wall Street and in Europe.
• U.S. futures fell on Monday evening after the market close.

SINGAPORE — Asia-Pacific markets traded mixed on Tuesday as investors remained cautious over rising coronavirus cases, U.S. stimulus negotiations as well as Brexit talks between the U.K. and the European Union.

Japan's Nikkei 225 fell 0.3% to 26,467.08 while the Topix index was down 0.11% at 1,758.81.

In South Korea, the Kospi declined 1.62% to 2,700.93 as the number of daily reported cases of Covid-19 remains high. The country reported 594 new coronavirus cases on Tuesday, including 566 domestically transmitted infections, Yonhap reported.

South Korea in recent weeks has seen a surge in infections and health officials warned daily cases could near 1,000 next week unless the spread is brought under control, according to Yonhap. The country has enacted strict social distancing measures around Seoul and other areas.

Australia's benchmark ASX 200 gained 0.19% to 6,687.70. The energy subindex declined 1.25% as oil prices remained under pressure during Asian trading hours.

Oil stocks in Australia declined: Shares of Santos fell 1.98%, Oil Search was down 1.57% and Woodside Petroleum fell 0.17%. Woodside's CEO Peter Coleman is set to retire in 2021.

In Hong Kong, the Hang Seng index fell 0.72% in late-afternoon trade. The health-care arm of Chinese e-commerce giant JD.com made its trading debut in Hong Kong and saw its share price surge compared to the company's issue price.

Chinese mainland shares were mostly lower: The Shanghai composite fell 0.19% to 3,410.18 while the Shenzhen composite and the Shenzhen component finished near flat.

Major indexes in India and Indonesia were also up in afternoon trade.

Tuesday's session in Asia-Pacific followed a mixed overnight session on Wall Street and in Europe. U.S. futures fell on Monday evening after the market close.

"Markets had a mixed session overnight," Cherelle Murphy from ANZ Research wrote in a morning note. "Negotiations over a new pandemic package continue in the US, while high (Covid-19) numbers and disappointing labour market data cast a shadow." A deal is widely expected by mid-December, Murphy added.

"UK-EU trade talks appear to be on the brink of collapse, with news expected this morning," Murphy said.

The U.K. and the European Union are making last efforts to reach a post-Brexit trade deal this week. Both sides remain divided over three issues: fisheries, competition rules and governance of their potential deal. They have been stuck on these three areas since early summer.

British Prime Minister Boris Johnson is set to travel to Brussels this week in a final push to clinch a post-Brexit trade deal with the EU. Johnson will meet European Commission chief Ursula von der Leyen in person after two phone calls between the leaders failed to bear fruit.

The British pound traded at $1.3341, down from an earlier level around $1.3377.

Currencies and oil

The U.S. dollar index, which measures the greenback against a basket of its peers, last traded at 90.907, climbing from its previous close at 90.792.

The dollar is "caught between the near term headwinds of a 'pull' of rising (Covid-19) cases and simmering US‑China tensions and the 'push' of vaccines improving the medium‑term economic outlook and expectations for more US fiscal stimulus," currency strategists at the Commonwealth Bank of Australia wrote in a morning note.

Elsewhere, the Japanese yen changed hands at 104.10 per dollar, weakening from an earlier level around 103.94, while the Australian dollar fell 0.18% to $0.7407.

Oil prices declined Tuesday during Asian hours: U.S. crude was down 1.09% at $45.26 as of 3:29 p.m. HK/SIN while the global benchmark Brent fell 1.19% to $48.21 a barrel.