She also said the yuan could become a global reserve currency if China implemented market-oriented changes.
Ms Lagarde is on a visit to China and India that began over the weekend.
Speaking to politicians and business leaders in Beijing she said there were signs the global economy was stabilising.
Ms Lagarde stressed that at the highest levels, China leadership appears to be willing to make the changes needed to ensure that the world’s second-largest economy remains a main driver of global growth.
As part of her short visit, Ms Lagarde met Vice Premier Li Keqiang – who is expected to become the China’s premier when Wen Jiabao steps down in a leadership change – Vice Premier Wang Qishan and Zhou Xiaochuan, governor of the central bank.
She said the world economy has “stepped back from the brink, and we have cause to be more optimistic”.
However, she added a word of caution.
“The global economy may be on the path to recovery, but with not a great deal of room for manoeuvre, and certainly no room for policy mistakes.”