But Lagarde did not say if the Indian government backed her candidacy, adding that many countries would wait until June 10 before announcing who they would support.
"Many African countries have expressed, publicly for some and privately for others, their support for my candidacy," Lagarde told CNBC TV.
"My suspicion frankly, is that a lot of countries are going to wait until June 10, because that is the closing of candidacy filing," she added.
Lagarde described her meetings with Indian officials as "excellent." She is in India seeking support for her candidacy.
"I don't think I will betray their confidence in saying that they (Indian leaders) expressed positive views about my skills and credentials," she said.
Lagarde added that a pending legal case in France involving her would not be an issue for her candidacy and that the case had no grounding.
Finance Minister Pranab Mukherjee told reporters earlier on Tuesday that India had not given any commitment to support Lagarde.
(Reporting by Manoj Kumar and Rajesh Kumar Singh; Editing by Alistair Scrutton)