Mr Papaconstantinou (right) has asked for more bail-out details
Greece has been warned by European finance ministers that it must make further cuts to spending and public sector wages or face more sanctions.
A joint statement from the 16 eurozone nations it said Greece needed to get its debt under control and calm "irrational" financial markets.
Last week, the European Union vowed to help Greece if needed.
But the idea of bailing out a euro nation has been badly received, prompting a harsher stance.
Greece's woes have sent the value of the euro down to a nine-month low recently.
Now the country has been told that further measures will be imposed if its debt reduction plans are not on target by 16 March.
Ministers and bank officials from the eurozone met in Brussels on Tuesday.
Germany's deputy finance minister, Joerg Asmussen, said Greece should follow the actions of Ireland and Latvia - both of which are making major cuts to spending and wages.
"We made it clear the ball is in Greece's court," he said. "Additional measures by Greece are needed".
Austrian Finance Minister Josef Proell said: "The pressure on Greece to consider further measures has clearly increased."
Earlier, Jean-Claude Juncker, chairman of the 16 nations that share the single currency and also Luxembourg's prime minister, told German radio that Greece must understand that other eurozone members were not prepared to pay for its mistakes.
Greece's debt crisis is "first and foremost a Greek problem and an internal Greek problem," Mr Juncker said.
"The financial markets are completely wrong if they think they can destroy Greece," he added.
Europe's leaders pledged to help Greece last week - without spelling out exactly what they were willing to do.
On Monday, French Finance Minister Christine Lagarde told reporters: "We won't abandon Greece. It's clear that we are all in this together."
Greece is trying to reduce its public deficit from 12.7% - more than four times the level that single currency rules allow.
It has pledged to reduce this to 8.7% during 2010 under an austerity plan that involves major cuts in public spending.
But those plans are hugely unpopular with the Greek public and strikes have already been scheduled.
Greek bank shares fell again on Tuesday on the continuing concerns.
The country's main stock index is down 14.6% so far this year.
On Monday, Greece's Finance Minister, George Papaconstantinou, said that he wanted the other eurozone nations to release details of their planned bail-out for his country to ease market fears that the country could default on its debts.
But Mr Juncker said it would be "unwise" to publicly detail "the measures we are putting in place".
Mr Papaconstantinou has said repeatedly that his country is not asking for financial help from Brussels.