Asian shares edged lower on Tuesday, while U.S. stock futures rose after President Donald Trump postponed a planned 50% tariff on EU imports, extending the deadline to July 9. The delay boosted risk sentiment, driving Nasdaq futures up 1.26%, S&P 500 futures up 1.11%, and FTSE futures up 0.94%.

Japan's Nikkei slipped 0.15%, and yields on super-long Japanese government bonds fell from recent highs. MSCI's Asia-Pacific index excluding Japan dipped 0.17%, while China's CSI300 dropped 0.06%, the Shanghai Composite was flat, and Hong Kong's Hang Seng Index declined 0.1%.

Markets were thin following Monday's U.S. and UK holidays. Investors are now eyeing Nvidia's Q1 earnings report on Wednesday, where the AI chipmaker is expected to post a 65.9% revenue jump. Month-end portfolio rebalancing and U.S. macroeconomic data -- especially Friday's core PCE price index -- also remain in focus, alongside several upcoming speeches from Federal Reserve officials.

In currency markets, the U.S. dollar struggled and was on track for a fifth consecutive monthly loss -- its longest losing streak since 2017. The euro traded near a one-month high at $1.14035, and the yen strengthened to 142.18 per dollar. Analysts attribute the dollar's weakness to erratic U.S. trade policy, ballooning fiscal deficits, and waning safe-haven appeal.

Gold prices, benefiting from dollar weakness, reached record levels earlier this year but slipped 0.28% to $3,332.91 per ounce.

Meanwhile, oil prices dipped slightly ahead of the upcoming OPEC+ meeting. Brent crude futures eased 0.1% to $64.67 a barrel, while U.S. WTI crude dropped 0.16% to $61.43.

Investor attention is also on the Bank of Japan's two-day conference in Tokyo, where global central bankers are discussing sluggish growth and persistent inflation.