Any steps the ECB takes to support the still-fragile euro zone economy could benefit some assets, though gains could be limited ahead of pivotal US payrolls data on Friday.
Japan's Nikkei share average gained 1.1 percent in early trade, while MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.4 percent to a nine-week high, with Taiwanese shares at two-year high
Wall Street shares finished little changed, with the Standard & Poor's 500 index closing just a hair's breadth below its record closing high set on Tuesday.
"The Ukraine crisis is not over yet so the markets will keep an eye on it. But as long as there is no armed conflict, it will be gradually coming off the radar," said a chief currency trader at a Japanese trading firm.
Although diplomatic efforts between Moscow and Washington over Ukraine have made little obvious headway so far, U.S. Secretary of State John Kerry said discussions would continue in coming days.
That assurance was enough to mollify investors' immediate fears of military confrontation, directing their attention instead to what steps the ECB might take to support the economy and ward off deflation.
The euro traded at $1.3728, little-changed in early Asia but off two-month high of $1.38255 hit on Friday.
On Wednesday, International Monetary Fund officials called on the ECB to start buying public and private assets or extend more cheap long-term loans to banks, as well as cutting interest rates to a new record low.
Yet the ECB may hesitate to buy government bonds, unlike other major central banks such as the U.S. Federal Reserve and the Bank of Japan that have done so, in part for fear such a step could infringe its ban on financing governments directly.
The ECB might explore other policy options, such as cutting rates or stopping "sterilisation" operations that soak up the money it spent buying the bonds of Greece and other countries at the height of the euro zone sovereign debt crisis.
"The chances the ECB will not do any of the steps floated in markets are pretty small. The actual economic impact of ending sterilisation will be small, but the markets will take it as opening the way for further easing in the future," said Arihiro Nagata, head of foreign bond trading at Sumitomo Mitsui Bank.
With the euro in retreat, the dollar index kept some distance from a two-month low hit last week, and was last at 80.164, versus Friday's low of 79.688.
Against the yen, the dollar held at 102.63 yen, near its highest level in about a week, reflecting abating concerns over Ukraine.
Likewise, U.S. 10-year bond prices fell back and yields lifted to around 2.70 percent, off a one-month low below 2.60 percent hit on Monday,
The yield rose despite soft U.S. data that nicked optimism over Friday's U.S. non-farm payrolls.
A report from payrolls processor ADP showed private employment increased by a tepid 139,000 jobs last month, with jobs growth in January also revised down sharply to 127,000 from 175,000.
A separate private-industry gauge of U.S. service sector activity also fell to its weakest level in four years in February, with its employment sub-index contracting for the first time since December 2011.
Still, the data did little to change investor perceptions that recent weakness largely reflected bad weather in the past two months.
Reduced fears over Ukraine led U.S. crude futures near a two-week low of $100.85.