But overall, movement was limited, as many dealers in Asia stood on the sidelines due to a market holiday in the United States, and waited for US consumer prices and growth data due later in the week to decide their stance on the dollar.
Some analysts said that the US currency, which has rebounded around five percent from a record low of $1.3670 per euro in late December, could soon resume its three-year descent.
"I think if there is a surprise this year its going to be on the downside on US growth," says Harvinder Kalirai, head of Asia Pacific research and analysis at State Street in Sydney.
"Once that becomes more evident we'll see a downward adjustment in US rate expectations, which would bring an end to the dollar's counter-trend rally that we've seen over the course of almost 2 months now."
The euro was little changed on the day at around 138.05 yen, near a 1 1/2-month high of 138.30 struck on Friday. Some dealers said there was ample room for the currency to climb to 140 yen in the near term.
"The euro isn't necessarily gaining because of euro-friendly factors," said Shogo Nagaya, forex manager at Nomura Trust and Banking.
"What we're seeing is selling in the yen versus the euro and other currencies," he said, adding that high-yielding currencies were the big winners on a quiet trading day.
The euro was down around 0.15 percent at $1.3055, just below a three-week high.
The dollar was barely changed at 105.70 yen. Disappointing Japanese gross domestic product figures and concerns about US deficits have sandwiched the dollar in the 105-yen range.
The Australian dollar bought around 83 yen a level not seen since mid-March 2004. The New Zealand dollar was at 72.35 US cents trading near a 17-year high.
The market has factored in a rise in Australian lending rates of 25 basis points as early as March. At 5.25 percent, Australian rates are more than double the 2.5 percent in the United States.
New Zealand rates are the highest in the developed world, standing at 6.5 percent, compared with near zero in Japan.
Dealers were showing increasing interest in carry trades, in which they borrow in a low-yielding currency to invest in one with a higher yield.
This was underlined by data showing speculators on the Chicago futures market took net long Australian dollar positions to a record high in the week ended February 15, while net short yen positions hit an 11-month low.
Long positions are bets that a currency will appreciate, while short positions anticipate losses in a currency. State Street's Kalirai, however, argued that the data showed the potential for a yen rebound. Any positive surprises for the yen could trigger a wave of short-covering.
US consumer price data on Wednesday will be closely watched, as higher inflation could prompt the Federal Reserve to accelerate its tightening campaign.
Also on Wednesday, the central bank will release minutes of the Federal Open Market Committee meeting on February 1-2. The Fed has raised rates six times since June.
The US government's second estimate for fourth-quarter gross domestic product growth is due on Friday.