Singh made the request when Karzai called him up to express condolence on the loss of Indian nationals in the attacks in Kabul yesterday.
Karzai promised "full investigation" into the incident, PM's Media Adviser Harish Khare said.
During the conversation, Singh conveyed India's "outrage" at the incident, he said.
While thanking the Afghanistan government for the assistance given, the Prime Minister requested Karzai to ensure full protection for Indian nationals in Afghanistan.
The two leaders agreed to stay in touch with other, he added.
Taliban carried out coordinated attack on two hotels in Kabul which had been rented out by Indians associated with the development works in that country. Up to nine Indians were among 17 people killed in the attack.
Singh yesterday condemned the terror strike saying it was a "senseless act of violence and barbarism" targeting those who were on a "mission of goodwill and friendship, helping to construct a peaceful, democratic Afghanistan that our Afghan friends desire".
Indians engaged in reconstruction and development tasks in Afghanistan have been repeatedly targeted by Taliban.