They said such a move was Ã¢â‚¬ËœessentialÃ¢â‚¬â„¢ to their decision to provide more resources to the International Monetary Fund (IMF) to help the region.
Earlier this month, eurozone leaders set up a permanent bailout fund of 500bn euro ($673bn; Ã‚Â£420bn).
There are concerns the fund may not be able to rescue a deeply indebted State.
“We have to see the colour of the eurozone’s money first Ã¢â‚¬â€ and quite frankly, that hasn’t happened.
“Until it does, there’s no question of extra IMF money from Britain or probably anyone else,” said British chancellor George Osborne.
Any move to boost the eurozone rescue fund is likely to put more pressure on the leading eurozone economies, especially Germany.
The eurozone’s biggest economy has so far resisted calls to increase the size of the bailout fund and sent mixed signals regarding whether it was prepared to change its stance.
On the eve of the G20 meeting, German finance minister Wolfgang Schauble wrote in an article published in the Mexican newspaper El Universal that he was against such a move.
“Should we increase even more the firewalls? The response is a resounding no,” he wrote.
“This would not only not solve the problems of debt and competitiveness that brought the affected countries to their current state of affairs, it would also discourage their governments from carrying out consolidation and reform.”
However, after the meeting, Schauble said that eurozone leaders would look into the matter and take a decision as early as next month.
Meanwhile, Olli Rehn, European Commissioner for Economic and Monetary Affairs urged the region’s leaders to solve the issue as soon as possible.
“One of the crucial lessons of this crisis has been that… the longer we wait the more costly it tends to get,” he said.
The eurozone debt crisis has seen growth slowing down in the region’s economies.
Italy and the Netherlands both slipped into a recession in the last quarter of 2011.
They saw their economies shrink by 0.7 percent during the three months to the end of December, the second consecutive quarter of economic contraction.Ã¢â‚¬â€Bbc