"Nobody believes that the Greek debt is sustainable," Euclid Tsakalotos said.
The far-left Syriza, which won Sunday's general election, wants to renegotiate Greece's €240bn (£179bn; $270bn) bailout by international lenders.
EU leaders have warned the new Greek government that it must live up to its commitments to the creditors.
Syriza leader Alexis Tsipras - who was sworn in as prime minister on Monday - is expected to unveil his new cabinet later on Tuesday.
"I haven't met an economist in their heart of hearts that will tell you that Greece will pay back all of that debt. It can't be done," Mr Tsakalotos said.
He said that EU leaders needed now to show that they were willing to work with Syriza.
"It's going to be a very funny and a very dangerous Europe with very strong centrifugal political forces if they signal that after a democratic vote they're not interested in talking to a new government.
"It will be a final signal that this is a Europe that can't incorporate democratic change and it can't incorporate social change."
But Mr Tskalotos stressed that it would be "my worst nightmare if the eurozone collapses because Greece falls".
"And if Greece falls and is removed from the eurozone - the eurozone will collapse. We said from the beginning the eurozone is in danger, the euro is in danger, but it isn't in danger from Syriza... it is in danger from the very policies of austerity".
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