MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.1 percent, and Japan's Nikkei advanced 0.2 percent.
S&P E-mini futures
Speaking at the U.S. Federal Reserve's annual conference in Jackson Hole, Wyoming, Draghi said the ECB's ultra-easy monetary policy was working and the euro zone's economic recovery had taken hold, but didn't cite the common currency's strength as a concern or discuss monetary policy specifically.
"The EUR bulls will feed off anything they can get that suggests a less accommodative stance going forward," Chris Weston, chief market strategist at IG in Melbourne, wrote in a note.
The dollar was slightly lower at 109.29 yen, adding to Friday's 0.2 percent slide after Federal Reserve Chair Janet Yellen, speaking at the same event as Draghi, also failed to address policy, focusing more on financial stability.
Yellen's remarks disappointed some investors who had hoped for hints on the Fed's plans for interest rates.
The 10-year U.S. Treasury yield
But lower bond yields helped give stocks a slight boost, with the Dow <.DJI> and the S&P 500 <.SPX> both ending about 0.15 percent higher on Friday, although the Nasdaq <.IXIC> closed about 0.1 percent lower.
Investors see a 40.7 percent chance of a rate hike by the Fed in December, down from 45.6 percent a month ago, according to the CME FedWatch tool.
The U.S. Gulf Coast, which includes Texas, is home to nearly half the United States's refining capacity, and the reduced output could affect gasoline supplies across the U.S. Southeast and other parts of the country.
Operators had shut down several refineries and evacuated offshore platforms last week as the storm crossed the Gulf of Mexico.
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