Asian shares started the week on a strong note on Monday after a weaker U.S. dollar helped fuel gains on Wall Street.

The greenback remained under pressure in Asian trading, with the dollar index .DXY edging down about 0.1 percent to 97.828, moving away from recent 12-year highs and back towards last week's low of 96.628.

Financial spreadbetters expected Britain's FTSE 100 .FTSE to open 17 to 21 points higher, or up 0.3 percent; Germany's DAX .GDAXI to open 2 to 7 points higher, or up 0.1 percent; and France's CAC 40 .FCHI to open 8 points higher, or up 0.2 percent.

"With the DAX above 12,000, FTSE above 7,000 and CAC above 5,000, there is a new sense of optimism in Europe," said Melbourne-based IG Markets strategist Stan Shamu.

European Central Bank President Mario Draghi was scheduled to testify on monetary policy to European Parliament's Economic and Monetary Affairs Committee.

"Given all the measures that have been introduced by the ECB and signs of bottoming in data, there is a good chance Mr. Draghi will give a more upbeat assessment of the economy," Shamu said in a note to clients.

MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS added about 0.5 percent. Chinese shares rallied on hopes of more support measures for the ailing property sector, with the Shanghai Composite Index .SSEC up about 1.5 percent, pushing to its highest in seven years.

But Australian shares turned negative, after the S&P/ASX 200 index .AXJO fell just a few points shy of topping the 6,000 level for the first time in seven years, prompting some investors to take profits.

Japan's Nikkei stock average .N225 ended 1.0 percent higher at 19,754.36, refreshing a 15-year high and closing in on its own big-figure milestone.

"Sentiment for Japanese stocks has been positive, and the 20,000-mark is in sight in the short-term," said Isao Kubo, equity strategist at Nissay Asset Management.

The dollar had been rallying against global counterparts in recent months on expectations that the U.S. Federal Reserve was preparing to hike interest rates this year, possibly as early as June.

Its weakness at the end of last week helped power Friday's gains in U.S. shares, as its strength raised fears about the profits of U.S. multinational companies.

The dollar plunged on Wednesday after the Fed cut its inflation outlook and its growth forecast. A majority of Wall Street's top banks now expect that the Fed will hold off raising rates until at least September, with the odds for a June hike fading, a Reuters poll showed.

"Due to the light economic calendar in the week ahead, the key issue facing market participants is whether the bout of profit-taking on long dollar positions is over," Marc Chandler, chief currency strategist at Brown Brothers Harriman in New York, said in a note.

Against the yen, the dollar stood at 119.90 yen JPY=, down about 0.1 percent on the day and well below Friday's session high of 121.205.

The euro traded at $1.0811 EUR=, down about 0.1 percent, though and well above a 12-year trough of $1.0457 logged a week ago, after which the Fed's statement helped it mark its biggest weekly rise against the greenback in three years.

Concerns about Greece's fiscal woes were likely to cap the euro's upside, even after European Union leaders welcomed a pledge on Friday from Athens to meet creditors' demands for a broad package of economic reform proposals within days to unlock the cash it needs to avoid stumbling out of the euro zone.

Commodity currencies benefited after the dollar's rally paused. The Australian dollar added about 0.4 percent to 0.7806 AUD=D4, well above a six-year nadir of $0.7561 hit on March 11.

Crude oil slipped on Monday after strong gains in the previous session as it benefited from the dollar's descent. Saudi Arabia said over the weekend that it would not unilaterally cut its output to defend prices.

Brent LCOc1 was down about 1 percent at $54.75 a barrel after snapping two straight weeks of losses, and U.S. crude CLc1 shed 1.6 percent to $45.85 after marking its first positive week in five.