Lagarde choice
The Prime Minister said the UK strongly backed the French finance minister and believed there was a "good case" for the role staying in European hands.
Mr Cameron said conversations with fellow leaders at the G8 summit had convinced him everybody believed she had "what it takes" to do the high-profile job.
Advertisement
Hide AdAdvertisement
Hide AdMs Lagarde is the overwhelming favourite in the race to succeed countryman Dominique Strauss-Kahn, who quit to fight charges of attempted rape in New York.
Mr Cameron said: "She has what it takes in terms of political leadership, experience and respect as a finance minister not just in Europe but more widely,"
However, some in the developing world want to break with tradition and see a non-European installed in the post.