The head of the group of Eurozone finance ministers has warned that there is little prospect of a deal which could see Greece writing off some of its national debt.
But Jeroem Dijsselbloem says EU officials will work with the new Greek government to see what can be agreed to deal with Greece's burden of debts.
The comments come as the far-left party Syriza agrees a coalition deal with the right-wing Independent Greeks, to seek a renegotiation of Greece's bailout deal.
The coalition agreement was sealed after a brief meeting between the two parties earlier this morning.
Syriza's leader Alexis Tsipras will now take an oath of office this afternoon to become Greece's prime minister.
His party swept to victory in yesterday's general election - taking 149 of the 300 seats available, just short of an overall majority.
Both he and his coalition partner were elected on a platform of renegotiating Greece's bailout packages, with a view to writing off some of the country's €320 billion in national debt.
While governments across Europe have acknowledged the Greek result and pledged to work with Mr Tsipras's new administration, there has been only a lukewarm response to the prospect of any further concessions to Greece - which has already been given extra time to repay its loans.
Speaking at a meeting of Eurozone finance ministers in Brussels, Mr Dijsselbloem said Greece might be able to delay some payments - but wouldn't be able to write off all of its debt.
"We already have done a lot to take off the debt pressure, the debt burden, by reducing interest rates, allowing longer periods for them to repay loans. There doesn't seem to be any great urgency there," he said.
But he added: "Writing off debt in nominal value? I don't think there is a lot of support for that in the Eurozone."
However he said ministers were prepared to discuss the 'sustainability' of Greece's debts - a nod to the prospect of further extending the repayment period to reduce the short-term demand on Greece's finances.
European Commission president Jean-Claude Juncker simply commented that the authorities in Brussels did not yet have "a relationship" with Greece's new government, as it had yet to take office.
In Ireland, foreign ministers minister Charlie Flanagan said a "debt conference", where Greece's creditors would attend talks to agree a write-off of some loans, was not in Europe's interests.
Our political correspondent Gavan Reilly filed this report for Today FM's National Lunchtime News:
