KIEV—The head of the International Monetary Fund Sunday praised Ukraine’s efforts to overhaul its economy, but urged Kiev to stay the course agreed upon with the emergency lender amid signs the coalition government may be beginning to fracture.

“To achieve what you have achieved in such a short period of time is just nothing but astonishing,” IMF Managing Director Christine Lagarde told Ukraine President Petro Poroshenko in a joint press conference.

The...