Greece's enormous debts are sustainable but on a "knife's edge," according to the International Monetary Fund.
A 110bn-euro (£96bn) rescue package for Greece is being implemented but investors still fear a default.
Given the situation, Greece must stick to its reform programme, IMF Athens mission chief Poul Thomsen said.
His comments came as UK Deputy Prime Minister Nick Clegg said he was "incredibly worried" about the Greek debt crisis.
Greece under Prime Minister George Papandreou has passed several rounds of austerity measures, including tax increases, pay cuts, privatisations and public sector redundancies, to get aid from the IMF and the European Union.
Poul Thomsen, the IMF's mission chief to Athens, said that Greece must now implement these reforms.
"Policies must be applied as planned, or the sustainability of the debt will be placed in doubt," he told Greek newspaper Ethnos.
"The Greek debt is sustainable but it is, as we say, on a knife's edge."
US Secretary of State Hillary Clinton said on Sunday on a visit to Athens that "the US strongly support the Papandreou government's determination to make the necessary reforms to put Greece on a sound financial footing".
Greece has more than 350bn euros of debt, and the IMF warned last week than it needs an additional 100bn euros in aid on top of last year's bail-out to avoid a default.
The eurozone members will hold a special summit on 21 July to discuss the debt crisis and provide fresh aid for Greece.
Mr Clegg told the BBC on Sunday that the crisis is "immensely serious".
"This has a direct impact on British jobs and the livelihood of people in this country," he said.
"I believe we should play an active role behind the scenes, because we are not a member of the euro, to help eurozone members make the reforms necessary to make a strong, prosperous eurozone in the future."
The Irish Republic and Portugal have had bail-outs since Greece received its aid package, and markets last week suggested they were worried that Italy will be the next.
On Friday, the European Banking Authority (EBA) said eight out of 90 European banks have failed stress tests designed to ensure they can withstand another financial crisis.
None of the tests included what would happen to the banks if Greece defaulted on its debt.
Five Spanish banks failed, as well as one in Austria and two in Greece.
The news came just as Italy's parliament approved a 70bn-euro austerity package.
According to the Bank for International Settlements, UK banks hold a relatively small $3.4bn (£2.1bn) worth of Greek sovereign debt, compared with banks in Germany, which hold $22.6bn,