Japan's Nikkei index led the advance, piling on 2.5 per cent as the yen sank, while a forecast-busting trade report from China also lifted spirits in Hong Kong and Shanghai, dealers said.
European markets were also up, with London receiving a boost also from far better-than-expected UK industrial production data.
At a meeting yesterday with airline executives, Trump said he would release details of a "phenomenal" tax cut plan in the next two or three weeks.
They continued rising at the opening bell today, with the Dow gaining 0.2 per cent.
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"US equities are adding to yesterday's rally following a promise of a "phenomenal" tax plan in the next 2-3 weeks by President Donald Trump, helping ease heightened trade and immigration concerns," said analysts at Charles Schwab brokerage.
World stock markets surged in the two months after Trump's November election win, buoyed by his promises to slash taxes, hike infrastructure spending and cut red tape to fan economic growth.
"Trump has started making the right noises again as far as markets are concerned, with today's promise of a 'phenomenal' tax announcement in the coming weeks certainly hitting all the right notes," said Craig Erlam, senior market analyst at Oanda trading group.
"Investors have become a little apprehensive in recent weeks due to the unpredictable nature of Trump's policies and the timing of the announcements which has taken the edge of moves we saw heading into year-end."
In a monthly update, the IEA added that oil demand was likely to be more vigorous than anticipated this year.