Cyprus a Sign of 'More Outbreaks' From Europe: New Zealand Minister

As equity markets recover from the shock delivered by the bailout plan for Cyprus that includes a levy on savers, New Zealand's Finance Minister says markets should not be surprised if more issues "pop up" from the euro zone.

"They've [the euro zone] got large, long running problems related to debt levels, which are still rising and they're not going to be resolved quickly," Bill English, deputy prime minister and finance minister of New Zealand told CNBC's " The Call " on Tuesday. "I think over the next five to seven years, you're going to see these occasional outbreaks of anxiety in quite unexpected ways."

English added that New Zealand was fortunate to be part of the Australasian banking system, which has strong banks.

"Our banks have been strengthening their position consistently over the last two or three years and there'll be no cause for concern in our market," English said.

The finance minister's comments come after global stock markets plunged on Monday in reaction to a weekend decision by euro zone ministers to force bank depositors in Cyprus to pay a levy of up to 10 percent of their savings as part of a bailout deal. That led investors to flee risk assets and pile into safe havens like gold, which hit a two and half week high, while the euro hovered around three-month lows against the U.S. dollar.

(Read more: Cyprus Bailout Crisis Slams Brakes on Risk-On )

Asian markets recovered some ground on Tuesday on news that lawmakers in Cyprus were trying to limit the impact of the levy on smaller depositors, but English said the Cyprus situation is a warning of what to expect from Europe going forward.

"Banks across Europe have been in trouble for some time and we shouldn't be surprised if occasionally the issue pops up and causes some real problems," English said.

In terms of the state of the New Zealand economy, where the government is aiming to return to a budget surplus in June 2015, English said the economy is still on track to achieve that goal.

"In New Zealand, there's strong political support to stop government debt rising and strong political support for the government cleaning up its expenditure to make sure we're getting value for money," English added.

In December, however, the government did cut its economic growth forecast to 2.3 percent from 2.6 percent for the year to March.

-By's Rajeshni Naidu-Ghelani; Follow her on Twitter @RajeshniNaidu