Lew adds his voice to warnings of a Greek 'accident'

U.S. Treasury Secretary Jack Lew said he feared Greece leaving the euro zone by "accident" and warned that the country and its creditors needed to "double down" their efforts so they can meet the next debt payment deadline.

Speaking at the London School of Economics, Lew said that a "miscalculation" at this stage could lead to a fresh crisis that could potentially be "very damaging".

Read MoreEl-Erian: Greece 'accident' 55% to 60% probability

U.S. Treasury Secretary Jack Lew
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U.S. Treasury Secretary Jack Lew

Lew's comments echoed those of chief economic adviser at Allianz, Mohamed El-Erian, who told CNBC on Tuesday that there was an increasing probability of a financial "accident" involving debt-strapped Greece.

El-Erian pegged the chances of an "accident"—in which Greek and European officials loose the ability to control Greece's future—at 55 percent to 60 percent, which he said was higher than what he had predicted just a few weeks ago.

Greece has come under renewed pressure this week that the country could be on the verge of quitting in the euro zone, after the country's interior minister, Nikos Voutsis, threatened over the weekend to default on loan repayments due to the International Monetary Fund (IMF).

Voutsis claimed the EU and IMF were pushing Greece to make unfair concessions in current bailout talks, without which some 7.2 billion euros ($7.87 billion) of aid frozen since last year would not be released, funds which Greece desperately needs to foot its bills.

But outspoken Greek finance minister Yanis Varoufakis tried to soothe fears late on Tuesday, dismissing previous comments on missing the deadline, adding that he was confident that the country will have reached an agreement with its creditors in early June.

Athens' next tranche of debt is a payment of 300 million euros ($326 million) to the International Monetary Fund, with a total of 1.6 billion euros owed to the fund in early June.

Read MoreVaroufakis battles 'divorce lawyer' style austerity talks

Greece's left-leaning government, led by Prime Minister Alexis Tsipras, has put forward new proposals for its budget to the IMF, with key sticking points in negotiations including pensions and sales tax.

Lew said while there had been progress in the debt talks, it was not enough for the issue to be resolved.

"I don't think anyone wants this to blow up. What I worry about is the accident. You have moments that come about at all too much frequency where just a miscalculation could lead to the crisis that would be potentially very damaging," Lew said.

"I think brinkmanship is a dangerous thing when it only takes one accident. I think everyone needs to double down and treat the next deadline as if it's the last deadline and get this resolved. The risk of going from deadline to deadline only increases the risk of an exit," said Lew.

Greek contagion heading your way?
Greek contagion heading your way?   

Contagion complacency 'mistake'

Lew warned against complacency over contagion from Greece, in a sentiment that was reiterated by the Canadian finance minister, who spoke to CNBC on Wednesday.

"There is a concern, even when you are dealing with a a very small country, that there will be broader implications," Joe Oliver told CNBC from the Group of Seven (G-7) meeting in Dresden, Germany.

"So in the interests of the Greek people and Europe generally, it is important that we deal with the shorter-term and longer-term aspects that are created."

Lew said it would be a "mistake" to think that a Greek default would have no repercussions outside of the country.

"The notion that risk is completely contained, that there's no contagion—I think it is a mistake to think that a failure is of no consequence outside of Greece," he told his audience at the London School of Economics.

Oliver added that there was a need for Greece to return to a sustainable economic path in order to avoid future shocks.

"We don't want to be back here five years from now confronting the same crisis in Greece, which while a small part of Europe, nevertheless can have implications more broadly," he told CNBC.

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