The euro last traded at $1.2861, up 0.1 percent on the day after a dip into negative territory, not far from Monday's low of $1.2829, its lowest since Nov. 22.
Many traders said they remained sellers of euros on any euro rebound while large option expiries were reported at $1.2750.
In Tuesday trade, the euro also hit multi-month lows against growth-linked currencies like the Australian and New Zealand dollars.
Investors were keeping a wary eye on developments in Cyprus, where the scheduled reopening of banks has been postponed to Thursday from Tuesday. Even then, banks will be subject to capital controls to prevent a run on deposits.
In Italy, a senior official in Silvio Berlusconi's center-right party said on Tuesday that there were still wide differences with the center-left that must be overcome this week or Italy will have to go back to the polls after last month's deadlocked election.
Stronger-than-expected data on U.S. home prices and new orders for long-lasting manufactured goods also underscored the divergence between the economy of the United States and the bleak outlook for the euro-zone economies.
(Read More: Home Prices Up, Best Yearly Increase Since 2006)
"Adding to the euro's bearish makeup is the region's struggle to recover from recession, and concern that political instability in Italy might soon lead to a credit ratings downgrade," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington, D.C.
Against the yen, the euro rose 0.4 percent to 121.44 yen, rebounding from a one-month low of 120.08 yen set on Monday, as the Japanese currency came under broad pressure. The dollar gained 0.3 percent to 94.45 yen.
BOJ's Kuroda said the central bank will seek to push down market interest rates by purchasing longer-dated government bonds, underscoring its resolve to expand its balance sheet more aggressively to beat deflation.
Some analysts cautioned that with market players already expecting drastic measures at the April 3-4 BOJ meeting, the yen could rebound if policymakers fail to produce a decision that matches those expectations.
Yen weakness was also limited by worries about the euro zone. The yen tends to benefit in times of market uncertainty as investors shed riskier investments funded by cheap borrowing in the Japanese unit.
"While Japanese policymakers have repeatedly expressed their preference for a weaker local currency in recent months, undercurrents of risk aversion emanating from the euro zone crisis have led to a good number of cross-border investors either taking profits on short-yen positions or even entering long-yen trades on a tactical basis," BNY Mellon wrote in a note to clients.
Analysts said flows related to yen repatriation ahead of Japan's fiscal year-end in March could also support the yen in the coming days.
Separate U.S. economic reports on Tuesday showed demand for long-lasting manufactured goods surged in February and single-family home prices started the year with the biggest annual increase in six and a half years.
(Read More: February US Durables Soar, Bolstered by Transportation)
The U.S. economy, however, is not out of the woods as other data showed consumer confidence tumbling in March while sales of new U.S. single-family homes fell more than expected in February after hefty gains the previous month.
(Read More: Confidence Tumbles in March as Consumers Turn Gloomy)
