Japan, China, Hong Kong, Singapore, South Korea and Taiwan are among the major centres in the region closed on Monday. Japanese and South Korean markets reopen on Tuesday.
"It's slow and likely to stay that way until at least the middle of the week when we get US retail sales, GDP from Japan and Europe and a BOJ meeting. So best to take a break and put your feet up for now," a trader in Sydney quipped.
The euro briefly plumbed $1.3325 in very early dealings after stop-loss selling was triggered below $1.3340, traders said. It then quickly recovered to around $1.3370, little changed from the New York close, where it idled for most of the session.
Since hitting a 15-month high of $1.3711 on Feb. 1, the single currency has shed about 2.5 percent. Last week, euro bulls took a bit more profit after ECB President Mario Draghi kept alive expectations of rate cuts. Draghi said the ECB would monitor the economic impact of a strengthening currency.
There are also growing worries about Spain as a scandal on secret cash payments engulfed the prime minister, while confidence in Italy has been shaken in the run-up to the Feb. 24-25 election.
A strong campaign by former Prime Minister Silvio Berlusconi has opened up the race and threatened the prospects of a stable government emerging after the vote.
"Better financial conditions are likely to be offset by rising political risks, market positioning and a weaker economy. We expect the euro to be on a declining trend beginning in Q2," said Aroop Chatterjee, analyst at Barclays Capital.
Against the yen, the euro was steady at 123.93, holding near Friday's one-week trough around 123.43. The dollar was at 92.63 yen, having plumbed a near one-week low of 92.17 Friday.
The yen found some support after Japanese Finance Minister Taro Aso said last Friday the currency has weakened more than intended following its recent eye-watering slide.
In the past few months, trading in the currency had been an easy one-way bet as Prime Minister Shinzo Abe put intense pressure on the central bank to take bold action to revive the fragile economy.
But this week is shaping up to be trickier as several event risks loom, not least the Bank of Japan's policy meeting on Thursday.
The BOJ is expected to keep monetary policy steady ahead of the G20 meeting starting Friday, particularly given that Japanese authorities have come under international criticism for allowing the yen to weaken.
There are also signs that Abe's push for a governor who will lead a radical policy shake up at the BOJ is meeting resistance from his own cabinet and financial bureaucrats.
"The yen remains our preferred funding currency, but we might see USD/JPY coming under pressure ahead of the G20 finance ministers meeting," analysts at Macquarie Bank wrote in a client note.
"This meeting will be an important test of policymakers' ability to refrain from exacerbating the currency wars currently being waged. An outside risk to this meeting is that the G20 unites to criticise Japan, which would lead to a stronger yen."
Following some action of its own last week, the Australian dollar found a tentative footing near $1.0300, with demand emerging whenever it falls below that level.
It skidded to a three-month around $1.0256 last week after the Reserve Bank of Australia left the door open to more rate cuts.