Without making a direct reference to the strident speech of his Pakistani counterpart Nawaz Sharif here yesterday in which he had insisted on a plebiscite in Kashmir, Modi made it clear that "raising issues in this forum is not the way to make progress towards resolving issues between our two countries".
In his maiden address to the 193-member UN General Assembly, the Indian leader underlined that his government placed the highest priority on advancing friendship and cooperation with its neighbours, including Pakistan.
Speaking in Hindi, Narendra Modi said, "I am prepared to engage in a serious bilateral dialogue with Pakistan in a peaceful atmosphere, without the shadow of terrorism, to promote our friendship and cooperation.
"However, Pakistan must also take its responsibility seriously to create an appropriate environment," he told the Assembly.
Narendra Modi's 35-minute address covered a number of subjects such as terrorism, including its resurgence in West Asia, reforms of the United Nations, including the Security Council, and the need for a more inclusive global development.
Talking about India's neighbourhood, the Prime Minister said that India desired a peaceful and stable environment for its development. "A nation's destiny is linked to its neighbourhood. That is why my government has placed the highest priority on advancing friendship and cooperation with her neighbours."
He told Pakistan that instead of raising issues at the UN, "today we should be thinking about the victims of floods in Jammu and Kashmir. In India, we have organised massive flood relief operations and have also offered assistance for Pakistan-occupied Kashmir".
"India is part of the developing world, but we are prepared to share our modest resources with those countries that need this assistance as much as we do," he said.
Describing the present as "a time of great flux and change", Modi said the world was witnessing tensions and turmoil on a scale rarely seen in recent history. Although there were no major wars "there is absence of real peace and uncertainty about the future".
He referred to the Asia-Pacific region and said that it was "still concerned about maritime security that is fundamental to its future."
While "extremism and fault lines" were growing in West Asia, Modi said, "our own region continues to face the destabilising threat of terrorism".
Modi told the General Assembly that terrorism was taking "new shape and new name" and no country, big or small was free from its threat.
He went on to ask, "are we really making concerted international efforts to fight these forces, or are we still hobbled by our politics, our division, our discrimination between two countries, distinction between good and bad terrorists"
Without naming Pakistan, the prime minister said even today "states allow terrorist sanctuaries on their territory or use terrorism as instruments of their policy".
In an apparent reference to the ongoing conflict in Iraq and Syria, where a US-led coalition is attacking the Islamic State (IS) militants, he said that India welcomed efforts to combat terrorism's resurgence in West Asia which was affecting countries near and far.
He pointedly emphasised, "this effort should involve the support of all countries in the region".
Pressing for a concerted international effort to combat terrorism and extremism, the Indian leader urged the world body to adopt the Comprehensive Convention on International Terrorism.
Calling for reform of the United Nations, including the Security Council, whose membership India is aspiring for, Modi said the world body should be more democratic and participative.
"Institutions that reflect the imperatives of the 20th century won't be effective in the 21st. It would face the risk of irrelevance and we will face the risk of continuing turbulence with no one capable of addressing it," he said.
* It is a matter of great pride that I am addressing the UN General Assembly as the Prime Minister for the first time, says PM Narendra Modi in his speech to the United Nations General Assembly.
* India sees the world as one big family, says Modi
* We believe in multilateralism, says Modi
* I am prepared to engage in a serious bilateral dialogue with Pakistan in a peaceful atmosphere, without the shadow of terrorism: PM
* Raising issues in UN is not the way to make progress towards resolving issues between our two countries: Modi
* Terrorism is taking new shape and new name. No country, big or small, in the north or the south, east or west, is free from its threat: PM.
* PM says it is important to expand the UN Security Council.
* We should think why despite the UN, we are making so many 'G' forums: PM.
* We should put aside our differences and mount a concerted effort to combat terrorism. I urge you to adopt the Comprehensive Convention on International Terrorism: Modi.
* When we craft agreements on international trade we should accommodate each other's concerns and interests, says Modi.
* The world should announce an International Yoga Day: PM