In Europe, shares rallied more than 1%, with many reaching their highest level since January 2018
Asian shares closed in on their July peak on Tuesday on increasing signs the United States and China are inching closer to a truce in their trade war and on optimism the US economy is well poised for solid, consumer-driven growth.
MSCI's broadest index of Asia-Pacific shares outside Japan was little changed in early trade after hitting a four-month high the previous day.
Japan's Nikkei .N225 rose 1.34% to one-year high after a market holiday on Monday.
On Wall Street, the S&P 500 .SPX gained 0.37% to a record high of 3,078.27 on Monday while the Dow Jones .DJI and the Nasdaq .IXIC also clinched all-time highs.
In Europe, shares rallied more than 1%, with many reaching their highest level since January 2018. The STOXX 600 index of small, mid-sized and large companies across Europe surged to highs last seen in July 2015.
US S&P500 futures ESc1 gained a further 0.2% in Asia after the Financial Times reported on Tuesday that the United States is considering dropping some tariffs on China.
The story came after Beijing and Washington spoke of progress in trade talks on Friday and US Commerce Secretary Wilbur Ross said licenses for US companies to sell components to China's Huawei Technologies Co will come "very shortly."
US employment data released on Friday showed strong job gains despite the drag from a strike at General Motors (GM.N), offering some assurance that consumers would continue to support the slowing economy.
"The data suggests the US is almost in a full employment. More importantly those strong numbers came after three rate cuts by the Fed," said Norihiro Fujito, chief investment strategist at Mitsubishi UFJ Morgan Stanley Securities.
"When the Fed did precautionary easing in the past - after Mexico crisis in 1994 and Asia/Russian crisis in 1997-98 - a rally in stock prices followed. No wonder money is flowing to risk assets now," he said.
Bonds are losing some of their appeal and the yield on benchmark 10-year notes rose back to 1.799% US10YT=RR compared to last week's low of 1.670%.
In the currency market, the dollar gained to 108.60 yen JPY=, extending its recovery from 107.89 touched on Friday.
Trade optimism kept the Chinese yuan near its highest levels since mid-August, with the offshore yuan at 7.0246 per dollar CNH=.
The euro changed hands at $1.1128 EUR=, off last week's high of $1.1175.
The Australian dollar traded at $0.68915 AUD=D4, staying near one-week low after a dire set of retail sales numbers released on Monday suggested the economy was still struggling despite three cuts in interest rates.
Still, that has did little to change market expectations that the Reserve Bank of Australia is expected to hold fire on Tuesday.
Oil prices held firm after hitting their highest levels since late September, buoyed by an improved outlook for crude demand as better-than-expected US jobs growth added to market hopes a preliminary US-China trade deal would be reached this month.
US West Texas Intermediate (WTI) crude traded at $56.56 per barrel, having hit a six-week high of $57.43 on Monday.