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The euro has been supported by lingering expectations of a near-term rate hike in the eurozone, while monetary policy tightening in the United States and Japan remains a distant prospect.
The euro was higher at $1.3819 compared to $1.3803. The unit rose to 113.40 yen from 112.85 yen.
Meanwhile the dollar firmed against the yen in Asian trade on Tuesday, supported by interest rate differentials between the United States and Japan, dealers said.
The dollar traded at 82.14 yen in Tokyo afternoon trading, up from 81.79 yen in New York late Monday.
Despite upheaval in Libya, the market has stabilised as US and Japanese stock markets score healthy gains and as a modest fall in world oil prices boosts sentiment towards the global economy, analysts said.
Crude prices on Tuesday were off highs seen last week after oil kingpin Saudi Arabia pledged to ensure sufficient supplies, partially easing investors' worries, they added.
Markets are looking ahead to key eurozone inflation data due later Tuesday for indications ahead of the ECB's policy-setting meeting this week.
"Investors' eyes are turning from the situation in the Middle East and North Africa to the monetary policy gaps," between global central banks' divergent approaches to inflation, said Teppei Ino, analyst at the Bank of Tokyo-Mitsubishi UFJ.
"In that sense, they are buying the euro for the dollar and the dollar for the yen," Ino said.
The European Central Bank will hold a policy meeting Thursday and ECB chief Jean-Claude Trichet is scheduled to speak after the meeting.
"The ECB is unlikely to raise rates at the upcoming meeting but will try to smooth the way for the move," Ino said. "The ECB's statement and Trichet's comments are therefore expected to have a hawkish tone."
The market is also looking ahead to US Federal Reserve Chairman Ben Bernanke's testimony to Congress Tuesday, amid concern about rising prices, dealers said.
Meanwhile, the Australian dollar weakened against the dollar after the Reserve Bank of Australia signalled it is unlikely to hike interest rates in the coming months.
After a regular policy-setting meeting the central bank left its cash rate target at 4.75 per cent, with governor Glenn Stevens noting that inflation is currently "consistent with the medium-term objective of monetary policy".
The Australian dollar dropped to $1.0160 following the statement, down from an earlier high of $1.0199.
The greenback was mostly lower against other Asian currencies.
The dollar fell to Sg$1.2707 from 1.2726 on Monday, to Tw$29.60 from 29.75 and to 30.59 Thai baht from 30.60. It also declined to 43.50 Philippine pesos from 43.71, but rose to 8,821.50 Indonesian rupiah from 8,812.50.
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