The common currency slid 0.2 percent to $1.1136 in its third session of declines after a German press report Athens may opt out of its next bailout payment.
Euro zone finance ministers failed to agree with the International Monetary Fund on Greek debt relief or to release new loans to Athens last week but did come close enough to aim to do both at their June meeting.
"The bailout payments are necessary to meet existing debt repayments due in July, so if Greece were to forgo this bailout payment the probability of a default would spike, reopening the discussion around a Grexit from the Euro-zone," said James Woods, global investment analyst at Rivkin in Sydney.
However, Woods cautioned against reading "too much into it" without more details or confirmation, adding that it is unlikely that Greece would opt out of the bailout payment at this stage.
A statement by European Central Bank President Mario Draghi reiterating the need for continued stimulus, and the prospect of early Italian elections also weighed on the euro.
MSCI's broadest index of Asia-Pacific shares outside Japan was flat early on Tuesday.
Japan's Nikkei slipped almost 0.1 percent.
China, Hong Kong and Taiwan markets are closed for holidays on Tuesday.
European blue-chip stocks fell 0.2 percent on Monday, with Italy's banking index sliding 3.4 percent, its biggest loss in nearly four months, after two lenders sought help to cover a capital shortfall.
Sterling retreated 0.2 percent to $1.281 after British Prime Minister Theresa May's lead over the opposition Labour Party dropped to 6 percentage points in the latest poll to show a tightening race since the Manchester bombing and a U-turn over social care plans.
The dollar inched back 0.1 percent to 111.15 yen in early trade.
The dollar index, which tracks the greenback against a basket of trade-weighted peers, advanced 0.2 percent.
In commodities, oil prices climbed in light trade but failed to make up last week's losses as concerns lingered about whether the extension of output cuts by OPEC and other producing countries will be enough to support prices.
US crude futures added 0.4 percent to $50 a barrel.
Gold was steady at $1,266.89 an ounce.
source: news.abs-cbn.com
