The IMF team is in Athens to provide financial advice
Greek government bond yields have hit new highs and Greek banks have asked for further government support as the country's financial woes continue.
The euro also slipped further against both the dollar and the pound.
The unwelcome developments came as a team from the International Monetary Fund (IMF) arrived in Athens for discussions with government officials.
Eurozone nations have agreed that if Greece needs aid, it should come partly from them and partly from the IMF.
Leading Greek banks asked for more than 15bn euros ($20bn; £13bn) of government support under a 28bn euro support scheme launched under the previous administration in 2008.
"They want to have additional safety now that the economy and banking system are under pressure," said Finance Minister George Papaconstantinou.
The continuing high yields on Greek government debt - the interest paid to investors for lending the government money - makes it harder for the state to borrow money to fund its budget deficit.
The rate for 10-year borrowing hit 7.2% at one point on Wednesday, a sign that markets have become more worried that Greece might default on its debt.
There is a risk here of a self-fulfilling prophecy.
The worry about a default forces borrowing costs up, further stretching the Greek government's financial position and increasing the danger that it will not be able to repay its debts.
The situation is further exacerbated by the economic weakness of the wider euro area.
New revised figures for the final quarter of last year show that economic growth ground to a halt.
The IMF said its team was in Greece to give advice on improving the management of the government's finances.
Whatever the official purpose of the IMF team in Athens, it could turn out they are preparing the way for a rescue loan, which would be the first for a country using the euro.
Concerns over such a rescue meant the euro fell slightly against the dollar to $1.3355. Against the pound it also fell, to 87.602 pence.