Eurozone finance chief Jean-Claude Juncker has said the Greek people have to be aware the country is facing its "last chance".
After a meeting with Greek Prime Minister Antonis Samaras, Mr Juncker praised the nation's "tremendous efforts" so far to cut its deficit.
But he said "priority number one" was further consolidation of the public finances of Greece.
He added that Athens must put in place economic and structural reforms.
These include changes to the labour market, and the relaunching of privatisation programmes which have been promised but not enacted.
Mr Samaras promised that Greece would finalise a package of cuts worth 11.5bn euros (£9.1bn: $14bn) in the next few weeks.
He wants an extension of up to two years to implement those painful cuts.
But Mr Juncker, who is also Luxembourg's prime minister, said a decision on that would depend on a report from Greece's main lenders, due next month.
"I have to underline this will depend on the findings of the troika mission and we have to discuss the length of the period and other dimensions," Mr Juncker told a news conference alongside Mr Samaras.
The troika of international lenders - the European Central Bank, the International Monetary Fund and the European Commission - will return to Greece next month to assess whether the country is on target to meet the conditions of its bailout.
Mr Samaras said he had also told Mr Juncker that Greece was serious about tackling tax evasion, while at the same time looking to provide security for its citizens.
"I talked to him about the serious, active, measures we are making as a country," Mr Samaras said.
He said that the three parties of the ruling coalition were also fully behind the package of cuts being implemented.
His country was "turning the page, economically, politically and socially", said Mr Samaras.
"The meeting was very fruitful," he added. "He [Mr Juncker] was able to update us about... the expectations that Europe has for Greece."
He said as well as Greece's debt, the pair also discussed the availability of finances for Greek businesses, with Mr Samaras saying that small and medium-sized firms in the country were "asphyxiating" because of a lack of funds.
On the wider issue of whether there was a danger of Greece leaving the euro, Mr Samaras said he was "confident that all those betting on a Greek exit - undermining our efforts - will be proven wrong".
"We will prove them wrong through our deeds, not just our words," he added.
Mr Juncker also said that he was "totally opposed" to a Greek exit from the eurozone.
Later this week Mr Samaras will also meet Germany's Chancellor Angela Merkel and French President Francois Hollande.
At issue during the week of talks is whether Greece will receive its next instalment of loans worth 31.5bn euros that it needs to avoid defaulting on its vast public debts.
Under the terms of the bailout agreement, Greece needs to demonstrate it can find 11.5bn euros in public spending cuts within two years in order to qualify for the money.
There are also reports that due to the worsening state of the economy, which affects tax receipts and welfare spending levels, Greece may now need to find savings of up to 13.5bn euros, 2bn more than thought.
Eurozone leaders have so far resisted any move to soften the bailout conditions, especially in Germany, where the government is under pressure not to make any more concessions.