Chinese markets, however, made a partial recovery after declines in the previous session that followed the country's central bank cutting the reserve requirement for banks over the weekend.
The Shanghai composite rose by 0.17 percent to close at around 2,721.02 while the Shenzhen composite lost its earlier gains to end largely flat at about 1,385.09.
Behind the Chinese market moves
"China's latest RRR cut of the year has not managed to boost the confidence," Huani Zhu from Mizuho Bank wrote in a Tuesday morning note. "Despite several rounds of RRR cuts, onshore credit condition remained somewhat tight, especially for (small and medium enterprises)."
Zhu explained that compared to the state-owned firms, private companies and SMEs were more likely to be hit the hardest in the protracted trade conflict with the U.S., given "less robust exports prospect, rising financing cost and softening sentiment."
Commenting on the impact of the move by the Chinese central bank on the slide seen in the mainland markets yesterday, BlackRock's Head of China Equities Helen Zhu told CNBC's "Squawk Box": "I don't think the reaction was really to the PBOC move."
Pence had accused China last week of "malign influence and interference," saying that the country was waging a sophisticated effort to sway the elections against the Republicans in retaliation for U.S. President Donald Trump's trade policies, according to a Reuters report.
China's on-shore yuan was at 6.9203 against the dollar as of 3:06 p.m., near similar levels as the off-shore currency. Before the market opened, the PBOC set the yuan mid-point at 6.9019 against the greenback, which was a bit weaker than a Reuters estimate of 6.8943 per dollar.
Track markets across the region
Australia's ASX 200 was down by 0.97 percent to close at 6,041.1 as the heavily weighted financial subindex fell 0.87 percent. Major banking names were lower, with Commonwealth Bank shares declining 0.87 percent. The lender said on Tuesday that it will unwind a controversial system of charging customers commissions on financial products, according to Reuters. The changes were sparked by damaging revelations from an inquiry into financial sector misconduct, the news wire reported.
Japan's Nikkei 225 closed lower by 1.32 percent at 23,469.39 and the Topix index fell 1.76 percent to end the trading day at 1,761.12. As of 2:56 p.m. HK/SIN, Hong Kong's Hang Seng index continued to beat the general downward trend to trade slightly stronger despite losing its earlier gains.
South Korea's markets were closed for a public holiday.
Currencies and oil
The Japanese yen traded at 113.24 against the dollar, strengthening from levels above 114.0 last week. The Australian dollar, meanwhile, traded largely flat at $0.7073.
Oil prices advanced further on Tuesday afternoon during Asian hours, with U.S. crude futures adding 0.74 percent at $74.84 at 2:53 p.m. HK/SIN and global benchmark Brent crude futures gaining 0.74 percent to $84.53.
— Reuters contributed to this report.