PM's media adviser Harish Khare, who revealed the details on the conversation between the two leaders, said that Karzai promised 'full investigation' into the incident.
Dr Singh has asked Karzai to ensure the safety of Indians in the country.
Khare also informed that the two leaders have decided to keep in touch with each other.
On Friday, Feb 26, the terror outfit Taliban launched coordinated attacks against two hotels in Kabul. These hotels were specifically struck as Indians, who were prime targets, associated with the development works in Afghanistan were put up there.
Reacting to the attacks earlier, Prime Minister Singh said that they were senseless acts of barbarism aimed at those on a "mission of goodwill and friendship, helping to construct a peaceful, democratic Afghanistan that our Afghan friends desire".