MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.2 percent in early trading, while Japan's Nikkei share average also slipped 0.2 percent.
Philippine shares bucked the downtrend, with the main index up 0.13 percent to 7,886.44 in early trading.
On Tuesday, the benchmark S&P 500 posted its biggest one-day drop in about six weeks and closed at its lowest point since May 31, after the US Senate's move to delay voting on a healthcare reform bill rekindled worries on the timeline for President Donald Trump's business-friendly policies.
US stocks accelerated their losses after Senate Republican leader Mitch McConnell decided to put off a planned vote on a bill to dismantle the Affordable Care Act until after the Senate's July 4 recess, to get more time to garner sufficient votes for its passage.
Against the perceived safe-haven yen, the dollar slipped 0.3 percent to 112.120 after rising as high as 112.285 yen.
The dollar index, which gauges the US currency against a basket of six major counterparts, edged up 0.1 percent to 96.442 but was still well below its previous session high of 97.447.
The euro was up 0.4 percent at $1.1339. It notched a 10-month high of $1.1345 after Draghi, speaking to a conference in Portugal, said the ECB could adjust its policy tools as economic prospects improve in Europe.
Some strategists said that once the dust settled from the impact of his comments, the euro could give back some of its gains.
"These weren't very hawkish comments, as he suggested some changes to policy although the overall stance did not change," said Masafumi Yamamoto, chief forex strategist at Mizuho Securities in Tokyo.
"To me, it seems the change in policy will not be very substantial, so I think in the coming days, ECB officials will try to water down Draghi's comments," he said.
Crude oil futures dropped, giving back some of their overnight surge. Prices rose nearly 2 percent on the weaker dollar, short-covering and expectations that US crude inventories might decline for a third consecutive week.
Brent crude futures fell 0.6 percent to $46.35 per barrel. US crude futures were down 0.9 percent at $43.86. -- with ABS-CBN News
source: news.abs-cbn.com
