The terrorist group attacked a patrol outside Tungushe, a village 22 kilometres (13 miles) from the Borno State capital Maiduguri.
Nearly half a million people have been displaced this year in Burkina Faso alone. The landlocked country has become the new hunting ground for extremists linked to the Islamic State group and al-Qaida.
The Taj Mahal Palace in Colaba and the Taj Lands End in Bandra received the calls on their landlines. Police are in the process of identifying the caller, the report said. Security has been tightened around the famed Taj Mahal Palace hotel near Gateway of India, official sources said on Tuesday.
The village is about 60 kilometres (35 miles) from the border with northeast Nigeria, the springboard for Boko Haram raids and kidnappings in neighbouring countries.