French President Francois Hollande first wrote to Prime Minister Manmohan Singh to express regret over the incident, in which six other Indians were injured. He then called him personally Tuesday morning.
The prime minister is in Durban for the 5th BRICS Summit.
French Defence Minister Jean-Yves Le Drian telephoned Defence Minister A.K. Antony in New Delhi to convey his regret and sent out his condolences to the families of the two Indian nationals.
According to an official release, Antony told the French minister that the news of the incident and, in particular, the killing of Indian nationals was extremely distressing.
"He (Antony) asked that the French forces in the Central African Republic should ensure the proper treatment of the injured Indian nationals and also requested that necessary measures be taken to ensure the safety of the other Indian nationals," the release said.
Le Drian assured Antony that the French side was conducting a high-level enquiry into the incident and the Indian government would be informed about its outcome.
The incident took place at the airport in capital Bangui. The French, who have some 250 soldiers stationed at the Central African Republic Airport, were guarding the airport, Indian officials here said.
"While conveying his condolences, President Hollande assured the prime minister of his firm determination to investigate the tragic event and assured that the injured were under the care of French medical teams," a statement by India's foreign office said.
"The prime minister expressed his deep distress at the loss of innocent lives.
"He has directed that all efforts be made to ensure the safety of approximately 100 Indian nationals in the Central African Republic, mainly in and around Bangui," the statement added.
The Indian ambassador to the Democratic Republic of Congo, concurrently accredited to the Central African Republic, "is making necessary arrangements for the return of the mortal remains of the Indian nationals in accordance with the desires of their next of kin".
Officials said the French have termed the incident a result of mistaken identity.
Its troops were trying to defend the airport and French nationals in the city. There are some 1,200 French people in the country, most of them in the capital.
The Central African Republic is a landlocked country with Chad in the north, Sudan in northeast, South Sudan in the east, Democratic Republic of the Congo and Republic of the Congo in south, and Cameroon in the west.
Its President Francois Bozize fled to Cameroon after rebels overran the capital of the impoverished nation of some 4.5 million long wracked by rebellions.
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