By Agence France-Presse
Donald Trump on Monday said he would press ahead with 10 percent levies on another $200 billion of imports, prompting Beijing to target $60 billion of US goods with five to 10 percent taxes.
The developments were a clear step up in the months-long stand-off between the world's top economies but analysts said dealers had been expecting the measures and essentially took the lower rates as a positive sign.
Wall Street's three main indexes rallied and Asia picked up the baton.
Tokyo rose 1.8 percent in the afternoon, with a shift out of the safe haven yen supporting Japanese exporters, while by the break Hong Kong and Shanghai each added one percent.
Sydney rose 0.6 percent, Singapore was up 0.5 percent and Taipei increased 0.7 percent. Wellington, Bangkok and Jakarta also posted strong gains but Seoul and Manila inched down.
"The bottom line why the market didn't react negatively was the lack of shock and awe given the tariffs were so well telegraphed," said Stephen Innes, head of Asia-Pacific trade at OANDA.
Dealers are now keeping an eye on possible talks between Washington and Beijing after US Treasury Secretary Steven Mnuchin sent an invite to avert a trade war, which many fear could destabilise the world economy.
"It's more likely that there will be some negotiated resolution coming through in the near term," George Schultze, founder and CEO of Schultze Asset Management in New York, told Bloomberg TV.
"Cooler heads will eventually prevail because otherwise both sides are shooting themselves in the foot."
However, Innes warned of further upheaval for investors.
"Despite the market taking the bluster in stride, history tells us that tariffs are detrimental for global trade and commerce," he said. "As such the current levels of market buoyancy belie the possible groundswell that could overrun markets."
On oil markets, both main contracts were flat after rallying more than one percent Tuesday on the back of comments from OPEC kingpin Saudi Arabia that it is happy with prices rising above $80 a barrel.
On foreign exchanges, the broadly upbeat sentiment provided support to embattled high-yielding and emerging market currencies, with Indonesia's rupiah up 0.2 percent, the Australian dollar 0.3 percent higher and the Thai baht 0.1 percent up.
The Mexican peso, Russian ruble and South African rand were around 0.4 percent up.
Key figures around 0400 GMT
Tokyo - Nikkei 225: UP 1.8 percent at 23,832.28
Hong Kong - Hang Seng: UP 1.0 percent at 27,348.14 (break)
Shanghai - Composite: UP 1.0 percent at 2,726.27 (break)
Euro/dollar: DOWN at $1.1672 from $1.1680 at 2100 GMT
Pound/dollar: UP at $1.3153 from $1.3146
Dollar/yen: UP at 112.37 yen from 112.33 yen
Oil - West Texas Intermediate: UP five cents at $69.90 per barrel
Oil - Brent Crude: UP one cent at $79.04 per barrel
New York - Dow Jones: UP 0.7 percent at 26,246.96 (close)
London - FTSE 100: FLAT at 7,300.23 (close).