"The euro continued to rally as the ECB increased its inflation forecasts," ANZ Bank New Zealand senior economist Sharon Zollner and senior FX strategist Sam Tuck said in a note.
"Hopes rose that there may be a resolution to the ongoing Greek stand-off, with Draghi saying that determined efforts were being made to reach an agreement. This supported sentiment."
ANZ said the kiwi will probably trade between 62.80 euro cents and 64 cents today.
In New Zealand today, Auckland real estate agency Barfoot & Thompson is expected to release its monthly housing data at 10am while data on first quarter building work put in place will be published at 10:45am.
In Australia, trade and retail data for April is scheduled for release at 1:30pm New Zealand time. The New Zealand dollar slipped to 91.77 Australian cents from 91.96 cents yesterday.
The kiwi edged lower to 46.60 British pence from 46.69 pence yesterday ahead of the Bank of England policy review where no change is expected.
The local currency declined to 88.76 yen from 88.85 yen yesterday. The trade-weighted index weakened to 74.47 from 74.68 yesterday.