Here are the latest developments:
"Countries that provide large peacekeeping forces don't have adequate representation in decision-making bodies. Mandates are ambitious, resources inadequate," PM Modi said in his address at the summit. India has promised more troops and training for the peacekeeping force.
PM Modi and Mr Sharif, who were seated facing each other at the summit, had smiled and waved at each other. This was the first time they came across each other and there had been expectations that the two leaders, who also stayed at New York's Waldorf Astoria hotel, would shake hands.
Before the peacekeeping summit, PM Modi had held bilateral discussions with US President Barack Obama - their third meeting in more than a year.
After the meeting, PM Modi had said US and India shares an "uncompromising commitment" on climate change and thanked President Obama for supporting "India's permanent membership in a reformed United Nations Security Council".
India's national agenda to counter climate change not just involves generating renewable energy, but also a "transition to a more sustainable energy mix," PM Modi had said.
The Prime Minister's last day in the US had been packed with meetings with various world leaders, including his British counterpart David Cameron, French President Francois Hollande and Palestine President Mahmoud Abbas.
PM Modi's whirlwind visit to the US had included an address to the UN General assembly and a meeting with the leaders of the G4 nations - the four countries which support each other's bid to join the UN Security Council.
But the tour mostly devoted to a push for business, tech and diaspora. Day One of the visit had been reserved for a series of meetings with the top executives of the US, which had concluded with a massive interaction session and dinner with CEOs of Fortune 500 companies.
In the hectic 36-hour tour of California, the Prime Minister had met the top leaders of the IT industry, including Microsoft chief Satya Nadella and Apple's Tim Cooke. He visited the electric car plant of Tesla Motors and attended the push for start-ups in India, the Startup Konnect programme.
The highlights of his trip were the Townhall at the Facebook headquarters, a visit to the Google campus and the power-packed 60-minute address to 18,000 members of the Indian community at San Jose.
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