Van Rompuy's statement came after he had held talks with several European leaders including Nicolas Sarkozy, the French president, Angela Merkel, the German chancellor, and George Papandreou, the Greek prime minister.
In a joint news conference later on Thursday, Sarkozy said that the European Commission would monitor Greece's fiscal actions on a monthly basis, while Merkel said the decisions about the country had been underwritten by all 27 members of the EU.
Speaking to Al Jazeera from Brussels, Jackie Davies, a senior adviser to the European Policy Centre, said the outcome of Thursday's talks was a mixture of a deal and a holding statement.
"There are two key messages out of what has been agreed today," she said.
"The first is a message to Greece, 'we want to see concrete evidence that you are going to implement the necessary reforms, you are going to get your deficits down, we're going to monitor you.'
"Second message, and this is the clear message to the markets, 'if that doesn't work then we'll stand by, we will be ready to help you if necessary'.
"But what people here are really hoping is that this strong political statement might be enough, if it calms the market jitters ... but I think people here know that it almost certainly won't and there will be other stages to go.
"But for today, they are trying to do it without actually putting any money on the table."
No financial request
Greece's budget deficit for 2009 equalled 12.7 per cent of gross domestic product, more than four times the limit for EU member states.
Athens will need to borrow around $75bn this year to cover its deficit and refinance debts.
Van Rompuy said that Greece had "not requested financial support" and that the EU was expecting "rigorous" action from its government to tackle the country's problem.
|Greece's pledges to cut its deficit have elicited massive street protests by civil servants
He said Athens would have to implement all agreed deficit-cutting measures to reduce its budget gap by four percentage points in 2010, as recommended by the executive European Commission and that further measures would be needed.
"The commission will closely monitor the implementation of the recommendations in liaison with the European Central Bank and will propose needed additional measures, drawing on the expertise of the International Monetary Fund," he said.
"We fully support the efforts of the Greek government and their commitment to do whatever is necessary including adopting additional measures to ensure that the ambitious targets set in the stability programme for 2010 and the following years are met."
A first assessment will be carried out in March, Van Rompuy said.
Concerns over the Greek debt and other weak European economies made the euro reach an eight-month low against the US dollar last week.
Hamish Macdonald, Al Jazeera's correspondent in Brussels, said: "It is not just the Greek economy that is in trouble, Spain and Portugal have rising unemployment and spiralling national debt."
"The concern is that if there is a run on Greek government bonds, a loss of faith in the government, that there might also be a run on government bonds in Spain and Portugal, and that could spread further."
But Elena Salgado, the Spanish finance minister, said those concerns are unjustified.
"The Greek economy is very different to the Spanish economy," she told Al Jazeera.
"We have done a lot of investment in the last 10 years ... Our financial system is very sound. Our statistics are credible and correct. So our situation is not the Greek one."
Greece has debts that are expected to reach nearly $400bn this year.