On Tuesday, the euro struggled to stay above the $1.300 level against the dollar in Asia. This was after finance ministers of the eurozone rejected an offer by private creditors to restructure Greek debt, keeping alive default fears.

The single currency slipped as low as $1.2987 before steadying at $1.3005 after jumping more than 1 percent to a high of $1.3053 on the EBS trading platform on Monday as hopes of an eventual Greek deal drove a wave of short-covering.

"The euro's moves are familiar, with positive news leading some to cover their short positions, followed by a correction as investors sell into the rallies," said Koji Fukaya, chief currency analyst at Credit Suisse in Tokyo.

After a report rekindled fears that Portugal could be the next potential default candidate after Greece, the euro hit a session low.

The euro hit a near four-week high of 100.49 against the yen on Monday before retreating to a low of 100.03 yen and steadying at 100.19 in Asia.

On Monday, the euro's retreat helped the dollar index .DXY rise off a three-week low of 79.602 hit and the greenback fetched 77.03 against the yen.

"There was no movement" on dollar/yen, said Masashi Murata, a currency strategist in Tokyo at Brown Brothers Harriman. "That is a pair that is caught, for the time being, no matter what the news is and what risk does."