In a statement, Singh said he had received a letter from French President Francois Hollande expressing his regret about the deaths and assurances that the circumstances of Monday's shooting would be thoroughly investigated.
"The prime minister expressed his deep distress at the loss of innocent lives," said the foreign ministry statement issued late Monday.
"He has directed that all efforts be made to ensure the safety of approximately 100 Indian nationals in the Central African Republic," it added.
The French defence ministry has said the Indians were killed when troops shot at three vehicles approaching the airport in the capital Bangui who had ignored warning shots.
The shooting happened "in a particularly confusing situation" after French troops had themselves been fired upon "from an unknown source", it said.
Around 300 French soldiers were dispatched to the Central African Republic over the weekend to reinforce troops already present in the capital Bangui, which was seized by rebels on Sunday.
The United Nations has since called emergency talks after the bloody coup sent ousted leader Francois Bozize fleeing across the border.
The French defence ministry said it "shares the pain of the families and sends them – as well as Indian authorities – its sincere condolences", adding it had ordered a probe into the incident.