The former French finance minister, who takes over from compatriot Dominique Strauss-Kahn, arrived in Washington late Monday, and is expected to hold a press conference on Wednesday.
Lagarde faces a tough challenge in living up to the standard set by her predecessor who, despite losing the IMF top job amid a sexual assault scandal in New York, remains a widely respected economist.
French television station France 24 reports that Lagarde's primary challenge will be managing the Greek debt crisis.
In the coming days, the euro zone and the IMF are expected to send the country the next tranche of aid – 12 billion euros - from last year’s 110-billion-euro rescue package.
Lagarde has previously called on Greece to implement the reforms necessary to get its public finance sector back on its feet.
France 24 said Lagarde would also be looking to make more room for emerging economies at the IMF, and to establish her legitimacy in her new position, despite the fact she is not a trained economist.
Following her appointment, Lagarde said her “overriding goal” would be that the IMF “continues to serve its entire membership”. She also said she wanted to unify the IMF's staff of 2,500 employees and 800 economists and restore their confidence in the organisation.
The New York Times columnist Paul Krugman said there was concern that Lagarde may be too sensible and cautious in the current economically turbulent climate, describing Strauss-Kahn’s leadership as “open minded”.
Meanwhile in France, the lawyers representing Strauss-Kahn said in a statement that he planned to sue French journalist Tristane Banon for defamation, after she announced on Monday her intention to file a lawsuit against him for attempted rape.
Banon's lawyer, David Koubbi, said the proceedings would centre on the behaviour of Strauss-Kahn when Banon interviewed him in a Paris apartment in 2003.