The request was made by its External Relations Minister Mbella Mbella during a bilateral meeting with External Affairs Minister Sushma Swaraj on the sidelines of the ongoing third India-Africa Forum Summit (IAFS) here.
"There was a detailed discussion on how militancy was affecting countries like Nigeria and countries in the neighbourhood including Cameroon, Niger, Chad and Benin," Sanjiv Kohli, joint secretary (West Africa) in the ministry of external affairs, said in a media briefing.
"They wanted India to help them in capacity building in the defence sector so that the combined forces that are right now combating Boko Haram can be strengthened," he said.
According to Kohli, India has agreed to "look at their request positively".
Based in northeast Nigeria, the Boko Haram has been waging a war against the country's government since 2009, killing more than 13,000 people.
"In addition to (defence) capacity building, the other priority areas which Cameroon mentioned were education, health, agriculture, and infrastructure development," said Kohli.
"They also wanted India's assistance in the IT sector and Indian private investments in sectors such as roads and highways, port development, water and energy conservation."
Kohli said that India has promised them to assist them in various areas of priority that they have identified.
On Tuesday, a ministerial meeting of the foreign ministers of India and the African countries was held as part of IAFS 2015.
Addressing the gathering, Sushma Swaraj called for cooperation between India and African countries in the fight against terrorism.
"All our nations find themselves faced with the growing scourge of terrorism," she said, noting the "menace of non-state actors and cross-border terrorism has acquired a new dimension" and "undermines the peace and stability in our countries, which is essential for our development efforts".
She said due to the fast-growing linkages of terrorist groups across the globe, "we must step up our cooperation through intelligence exchange, training and other measures to counter this menace".
"We also hope that the international community will cooperate with urgency to adopt the Comprehensive Convention against International Terrorism," she said.