There had been fears that Greece had not been progressing fast enough with cuts and this would be delayed.
Meanwhile, reports suggest a new bail-out deal is being finalised.
"I expect the Eurogroup to agree to additional finance being provided to Greece under strict conditionality," said Jean-Claude Juncker, who is head of the group of finance ministers.
Speaking after a meeting with Greek Prime Minister George Papandreou, he said that conditionality would include further privatisations.
"On that basis, it's obvious there will not be an exit of Greece from the euro area, there will be no default and Greece will be able to fully honour its obligations," said Mr Juncker.
More aid Earlier media reports suggested that Greece had agreed in principle a new bail-out package with its European partners.
The reported new three-year plan would in effect supersede Greece's existing 110bn euro EU and International Monetary Fund bail-out, Reuters said.
Greece would target another 6.4bn euros in austerity measures and finally start its 50bn euro privatisation programme.
In return the country would be offered some form of reduction in its debts.
The broad terms of the package were agreed at a meeting of eurozone deputy finance ministers in Vienna that went on until after midnight on Thursday night, the report said.
Although the size of the new package was not revealed, the news agency source said it would cover Greece's borrowing needs for this year and next.
A report in the Greek newspaper Kathimerini said it would provide 85bn euros, of which 30-40bn would come as EU and IMF loans, with the rest coming from privatisation proceeds and from private sector debt relief.
Details of any new plan would still need to be finalised, so that it can be signed off by the Eurogroup of eurozone finance ministers when they meet on 20 June.
The blessing of the IMF and the European Central Bank is also likely to be needed.
The additional spending cuts and tax rises would come at time when the government already faces daily demonstrations by thousands of protesters against its existing plans.
On Friday, protesters from the pro-Communist PAME union blocked access to the finance ministry in Athens, and hung a banner from it calling for a general strike.
The previous night, about 20 protesters hurled stones and yoghurt at government spokesman George Petalotis as he was stepping up to the podium at an event for the ruling PASOK party.
Meanwhile, Mr Papandreou also faces the risk of a backbench revolt over his austerity plans.
A group of 16 PASOK MPs wrote to him calling for a full party debate on the new measures.
The government has a majority of 12 in the Greek parliament.
IMF threat The original bail-out plan has been overtaken by events, leaving the Greeks desperately short of money again.
The plan had envisaged Greece returning to the financial markets to help fund its deficit from next year.
But with its two-year borrowing cost currently at about 25%-per-year, the market is effectively closed to Athens. Earlier this week, ratings agency Moody's cut its rating of Greece to one of the worst levels available, on a par with Cuba, and only slightly above recently-defaulted Ecuador.Moreover, Greece has failed to bring down its deficit as quickly as planned, largely because its economy has remained mired in recession.
'Credit event' The new bail-out agreement is likely to include a "soft restructuring" or "reprofiling" of Athens' private sector debts, advocated by Mr Juncker as a way of making the nation's debt burden more manageable. Claudio Loser Former IMF director for the western hemisphere
Until now the idea has been fiercely resisted by the European Central Bank, which fears that by imposing losses on Greece's lenders - including overstretched European banks - the move could spark a broader eurozone financial crisis.But it appears that an agreement has now been reached to grant Greece debt relief, so long as it is done in a way that does not trigger a "credit event", according to the Greek government source quoted by Reuters.
This "credit event" could refer to the risk of triggering payments under derivative contracts used by financial markets to hedge or speculate on the risk of a Greek default.
It could also refer to methodologies used by the credit rating agencies and by the banks to determine whether loans are in default.
Many European banks have not yet recorded any losses on most of their lending to Greece, and could find their own solvency is put at risk if they are forced to do so.
It is likely that the restructuring would involve the postponement of debt repayments due in the next two years.
It would also have to be done with the agreement of Greece's private sector creditors.
But according to a former director of the IMF, Greece will eventually have to impose losses, or "haircuts", on its lenders - something that would definitely constitute a default.
Claudio Loser, who negotiated past IMF rescue loans for Argentina and Uruguay, said Greece's only other option was to abandon the euro, although he conceded this would be "more complicated".