The euro rose 1 percent to 135.96 yen, having hit a one-week low of 133.96 yen earlier. The dollar edged up 0.3 percent to 118.75 yen, crawling away from a 10-day low of 118.11 struck on Monday.
Greece faces the risk of running out of funds when its bailout package expires at the end of this month, but investors were taking the view that throughout the euro zone debt crisis crucial agreements have tended to be clinched at the last minute.
"Even though it is clear that euro zone politicians are head to head in a high stakes game, it is possible that many investors are taking the view that a deal is still likely," said Jane Foley, senior currency strategist at Rabobank.
"After all, throughout the euro zone crisis, political breakthroughs tended to be made only when tensions were at boiling point."
The next focus points on Greece will be on Wednesday and Friday. On Wednesday the European Central Bank decides whether to maintain emergency lending to Greek banks that are bleeding deposits at an alarming pace.
And Dutch Finance Minister Jeroen Dijsselbloem, who chaired the meeting with Greece, said Athens has until Friday to request an extension.
Read MoreWhat next for Greece after talks stall?