Japan's benchmark Nikkei 225 added 0.4% to finish at 21,260.14, while Australia's S&P/ASX 200 gained 0.5% to 6,484.80. South Korea's Kospi edged up 0.2% to 2,048.83. Hong Kong's Hang Seng added 0.4% to 27,390.81, while the Shanghai Composite rose 0.6% to 27,390.81.
On Wall Street, which had been closed Monday for the Memorial Day holiday, futures for the Dow were up 0.1% while those for the S&P 500 were up 0.2%. During a state visit to Japan, President Donald Trump pointed to the United States' continuing "unbelievably large" trade imbalance with Japan, but also said a trade deal was coming this year. The U.S. seems to want to limit its trade tensions with some countries as it focuses on a battle with China that ranges from tariffs to technological supremacy.
The U.S. and Chinese leaders are expected to meet in late June in what could be the next pivotal moment for the trade war and its impact on the economy and markets. In Europe, investors were still digesting the results of the vote for the European Union's parliament. Pro-EU forces retained a majority despite the rise of nationalist parties. That eases fears that nationalist parties might halt the bloc's integration, though anti-EU sentiment could yet create tensions.
ENERGY: Benchmark U.S. crude rose 41 cents to $59.04 a barrel. Brent crude, the international standard, added 2 cents to $68.79 per barrel. CURRENCIES: The dollar weakened to 109.43 yen from 109.53 yen Monday. The euro slipped to $1.1192 from $1.1193.