Lagarde, supported by the British finance minister, George Osborne, said the IMF could boost its support for the euro zone but pressed its leaders to act first. Some attendees at the Davos Forum still doubted the viability of the currency union.
Countries beyond the 17-country bloc want to see its members stump up more money before they commit additional resources to the IMF, which this month requested an additional 500 billion euros (USD 650 billion) in funding.
"Now is the time - there has been a lot of pressure building in order to see a solution come about," Lagarde told a Forum panel discussion on the economic outlook from which euro zone leaders - most notably Germany - were conspicuously absent.
"It is critical that the euro zone members develop a clear, simple firewall that can operate both to limit the contagion and to provide this sort of act of trust in the euro zone, so that the financing needs of that zone can actually be met," she said.
Lagarde's comments rounded out a crescendo of calls at the Davos Forum for the euro zone to boost its financial defenses. The annual five-day conference began with German Chancellor Angela Merkel deflecting pressure to do so.
In a carefully worded keynote address, Merkel suggested doubling or even tripling the size of the fund may convince markets for a time, but warned that if Germany made a promise that could not be kept, "then Europe is really vulnerable."
On Friday, US Treasury Secretary Timothy Geithner pressed Europe to make a "bigger commitment" to boosting its firewall.
Two bankers who attended meetings with Geithner at the Forum said on Friday the United States was looking for the euro zone to roughly double the size of its firewall to 1.5 trillion euros. There was no immediate comment from the US Treasury.
Osborne said the currency bloc must beef up its firewall before other countries increase their funding to the IMF.
"I think the euro zone leaders understand that," said Osborne, the only European minister on Saturday's panel discussion on the global economic outlook in 2012.
"There are not going to be further contributions from G20 countries, Britain included, unless we see the color of their money," he added, calling for the euro zone "to provide a significant increase in available resources."
More Optimism...For Some
Japanese Economics Minister Motohisa Furukawa echoed Osborne's comments, saying: "Without the firm action of Europe, I don't think the developing countries like China or others are willing to pay more money for the IMF."
On condition that the euro zone boosts its own defenses, he said Japan and other countries were willing to additional support via the IMF.
Lagarde said, however, that if the international lender's resources were boosted sufficiently, this would raise confidence to such a degree that they would not be needed.
"If it is big enough, it will not get used. And the same applies to the euro firewall for that matter," she added.
Japanese Prime Minister Yoshihiko Noda, speaking to the Forum by video link from Tokyo, said Japan was working with South Korea and India to reduce the risk of the euro zone crisis spreading to Asia.
"Japan stands ready to support the euro zone as much as possible," he added.
Mexico's central bank chief, Agustin Carstens, said on Friday he believed a consensus was building on boosting the IMF's resources to help European countries and others that might need aid from the global lender.
There has been a palpable sense of hope at the Davos Forum that the euro zone is pulling back from the brink of catastrophe, though business leaders are equally worried that Europe's woes will hold back a global recovery.
Osborne saw some signs of optimism.
"People have commented on the mood of this conference being quite somber but having been here for a couple of days people have also pointed out that actually people are slightly more optimistic at the end of the week than the beginning," he said.
However, Davos 2011 also ended on upbeat note about the euro zone and a feeling that worst of the crisis was over - only for the situation to deteriorate and financial markets to turn their fire on Italy, the bloc's third biggest economy.
"The euro zone is a slow-motion train wreck," said economist Nouriel Roubini, made famous by predictions of the 2008-09 global banking crisis.
He expected Greece, and possibly Portugal, to exit the bloc within the next 12 months and believed there is a 50 percent chance of the bloc breaking up completely in the next 3-5 years.
Hong Kong's Chief Executive, Donald Tsang, said no matter how strong the euro zone's firewall is, the market will look at the nature of the economies it is protecting.
"If it is protecting insolvent economies...no matter how strong the firewall is, it won't survive," he said.