The euro rose 1.3% against the dollar to $1.0868 at the close of NY trading, its biggest daily percentage gain since last June.
MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS rose 0.35 percent to its highest level in more than three weeks, marking four straight days of gains.
The Canadian dollar fell 0.5 percent to C$1.3561 per USA dollar aftre the United States announced new duties avearging 20 percent on Canadian softwood lumber imports. South Korea's KOSPI .KS11 also advanced 0.7 percent to the highest level since April 2015. French shares pulled back 0.1%, having risen 4.1% on Monday in their biggest daily gain since August 2012.
Against this backdrop, the bank has upped its year-end 2017 forecasts for both euro/dollar and sterling/dollar forecasts to 1.20 from 1.10.
The U.S. dollar gained against the loonie after the report, up 0.34 percent to 1.3546 after U.S. Commerce Secretary Wilbur Ross said on Monday his agency will impose new anti-subsidy tariffs averaging 20 percent on Canadian softwood lumber imports, a move that escalates a long-running trade dispute between the two countries.
U.S. President Donald Trump's promise of an announcement on a tax reform plan on Wednesday could offer further impetus to markets, she added.
Indonesian stocks .JKSE opened at an all-time high, and Malaysian stocks .KLSE hit their highest level since May 2015.
Markets in Australia and New Zealand are closed for ANZAC day.
Polls show Emmanuel Macron defeating anti-euro nationalist Marine Le Pen by as much as 30 percentage points in the second round of the French presidential election in two weeks. South Korea's defense ministry could not immediately confirm the report.
Pittsburgh Penguins superstars just too much for overwhelmed Columbus Blue Jackets
Penguins G Matt Murray remained out for the fourth straight game with a lower-body injury sustained before the series opener. But things got worse: the Penguins, essentially playing with a man advantage, tied up the game at 3-3 on a Bryan Rust tally.
On Sunday night, the pound spiked against the dollar to a high of $1.28632 before dropping dramatically to $1.27842. Sources close to the ECB's Governing Council told on Tuesday that with the fading of the threat of a run-off between two eurosceptic candidates in France, and with the economy on its best run in years, many rate setters see scope for sending a small signal in June towards reducing monetary stimulus.
The Nasdaq Composite hit a record high on Tuesday, while the Dow and S&P 500 brushed against recent peaks as strong earnings underscored the health of corporate America. The Canadian dollar was trading at C$1.3564 to the greenback, or 73.56 US cents, weaker than Monday's close of C$1.3516, or 73.99 USA cents. The dollar fell 0.4% against the Mexican peso and 1.9% against the Turkish lira. It retained most of Monday's 1.3 percent gain, which was its strongest one-day performance in 10-1/2 months, and lifted the common currency to a 5 1/2-month high.
The euro traded at $1.0863 against the dollar, off the five-month high of $1.0935 hit earlier.
A strong earnings season in the United States has also lifted investors' spirits, with 77 per cent of the 100 companies that have reported first-quarter results so far beating profit expectations.
Oil prices edged up in volatile trading on Tuesday, rebounding from six days of losses, ahead of USA crude inventory data forecast to show a drawdown.
USA crude CLc1 gained 0.5 percent to $49.47 a barrel, but hovered close to the lowest level in nearly four weeks hit on Monday.
USA crude futures settled up 33 cents to $49.56 a barrel, breaking a streak that saw the benchmark lose 7.4 percent.
Gold, sought as a shelter for wealth in turbulent times, fell 0.4% to just less than $1,270 an ounce.
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