The leaders, who held a telephone conference with Greek Prime Minister Georges Papandreou on last evening, said they were convinced that Greece's future is in the euro zone, a government spokesman said in Berlin.
They also underlined that it is essential "more than ever before" to fully implement the decisions of the euro zone leaders on July 21 to ensure the stability of the euro zone.
The euro zone heads of state and government had agreed at that meeting to expand the group's financial bailout fund from the present level of 440 billion euros to around 750 billion euros and to give new powers to the fund to buy sovereign bonds of cash-strapped member nations and to intervene much early to avert a debt crisis.
However, the proposed expansion of the European Financial Stability Facility (EFSF) is facing strong opposition in Germany, where a recent survey showed that more than 65 per cent of the population are against the plan.
Several members of Chancellor Merkel's Christian Democratic Union and its coalition partners have threatened to deny the government their support when it comes up for voting in Parliament at the end of this month.