Boris Schlossberg, managing director of FX Strategy at BK Asset Management in New York, said the euro could even rally after a knee-jerk move lower as some investors see a rate cut by the ECB as another effort to stimulate the euro zone economy.
"It's clear that the euro zone economy is really in a quagmire and it needs some kind of jump-start," Schlossberg said. "There's almost nothing else available. A rate cut is better than nothing."
(Read More: Italy Will Die From Austerity Alone: Prime Minister)
"Even though the market initially perceives the rate cut as a negative thing, it will actually be disappointed if they don't see the rate cut and that can drive the euro down."
Signs are growing that weakness in peripheral euro zone economies is spreading to the region's core, such as Germany, the region's biggest economy. Confidence in the euro zone fell more than expected in April, data showed on Monday, highlighting the souring mood among companies and consumers since March.
The euro was kast up 0.5 percent at $1.3099, with hedge funds cited among key buyers. The session peak of $1.3115, the highest since April 19, was reached midway through the London session.
Other investors, however, are arguing for broader dollar weakness after recent weak U.S. data, saying the euro could hold on to its gains.
The U.S. economy grew more slowly than expected in the first quarter, and with inflation anchored, expectations are fading that the Federal Reserve could cut back its quantitative easing program anytime soon.
"That is weighing on the dollar," said Ian Gunner, portfolio manager at Altana Hard Currency Fund In London.
Gunner said only a cut in the ECB's zero percent deposit rate, which he did not expect, would cause the euro to fall sharply.
A two-day Federal Reserve policy meeting beginning on Tuesday is also being watched. If the Fed flags fresh risks to growth, some of the long dollar positions put in place in recent months could be trimmed.
Against the yen, the dollar rose 0.1 percent, to 97.99 yen, erasing losses after stronger-than-expected data on sales contracts for previously owned U.S. homes.
(Read More: Pending Home Sales Tick Upward in March)
The dollar set a four-year high of 99.94 yen earlier in April after the Bank of Japan announced a major stimulus program.
The dollar has faced stiff resistance at 100 yen, but many expect it to firm against the yen as Japanese investors such as insurance companies and pension funds allocate some of their portfolios to overseas assets in coming months.
