In an interview with the BBC, Ms Lagarde said there had to be more tax collection and structural reform.
That is despite the deep unpopularity of austerity measures imposed on Greece by the IMF and European Union in return for bailout funds.
Greek politicians are divided over whether to continue supporting those measures and face a 17 June election.
"The Greek population has made huge efforts. But they have more to do. There are more structural reforms to be had, there is more tax to be collected and that has a price," Ms Lagarde said in an interview with the BBC's Today programme.
Many analysts think that Greece may abandon the austerity measures and be forced out of the euro.
Ms Lagarde said the IMF did not like the that prospect, but that it was "prepared for all possible situations".
But she said that the costs of Greece leaving could be so high that other members of the eurozone may be prepared to pay more to keep Greece in the euro.
"It may well be that members of the eurozone will be prepared to support financially more and maybe longer the Greek country and population to stay within the zone," she said.
Greece is likely to be discussed when European Union leaders gather in Brussels on Wednesday for a meeting.
It will be the first time the new French President, Francois Hollande, has attended an EU gathering of this kind.
It is thought that Mr Hollande will push for the creation of pan-European bonds.
That would allow struggling nations such as Spain and Italy to borrow much more cheaply on international money markets.
But German Chancellor Angela Merkel will not consider such a scheme until other EU nations have improved their finances and shown greater budget discipline.
Germany can borrow extremely cheaply on the money markets.
In an auction on Wednesday morning, it borrowed 4.56bn euros ($5.76bn) for two years at a record low interest rate of 0.07%.