He also called for concerted efforts to deal with the threat of terrorism.
In his address at the inaugural session of the Third India-Africa Forum Summit (IAFS), Modi said the world was undergoing political, economic, technological and security transition on a scale and speed rarely seen in recent history and yet the global institutions reflected the circumstances of the century that "we left behind".
The summit, biggest such event organised by India in three decades, was attended by representatives of over 50 countries including 41 Heads of State and Government of African countries.
"This is a world of free nations and awakened aspirations. Our institutions cannot be representative of our world, if they do not give voice to Africa, with more than a quarter of UN members, or the world's largest democracy with one-sixth of humanity. That is why India and Africa must speak in one voice for reforms of the United Nations, including its Security Council," Modi said.
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"Today, in many parts of the world, the light of a bright future flickers in the storm of violence and instability. When terror snuffs out life on the streets and beaches, and in malls and schools of Africa, we feel your pain as our own. And, we see the links that unite us against this threat.
"We also see that when our oceans are no longer safe for trade, we all suffer together. And, when nations are caught in conflict within, no one around remains untouched. And, we know that our cyber networks bring opportunities, but also carry huge risks. So, when it comes to security, distance no longer insulates us from each other," he said.
"We will also provide support for African Union's peacekeeping efforts. And, we will train African peacekeepers here and in Africa. We must also have a stronger voice in decisions on UN Peacekeeping Missions," he said and noted that Africa has its concerns about security and stability, especially from terrorism and extremism and hoped its leadership will rise to the challenges.