During the meetings, Sri Lanka President Mahinda Rajapaksa, Bangladesh Prime Minister Sheikh Hasina and Nepal Prime Minister Sushil Koirala congratulated Modi on his first UN speech and promised full support for his initiative of having an International Yoga Day.
Modi reaffirmed his commitment to make the South Asian Association for Regional Cooperation (SAARC) a strong regional block.
The three leaders also said that they were looking forward to Modi's visit to their respective countries, including for the SAARC summit in Nepal later this year.
The Prime Minister also enquired about the status of bilateral projects he had announced during his Nepal trip.
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Ministry of External Affairs spokesperson Syed Akbaruddin said that Modi in his meetings with the three neighbouring leaders discussed various other issues of common concerns for SAARC block and reiterated his commitment to 'neighbours first' policy.
The South Asian leaders congratulated India on its recent Mars orbiter mission and said they were looking forward to progress on SAARC satellite mission announced by Modi earlier.
This was the second meeting between the two leaders after Modi was sworn-in on May 26 this year.
Rajapaksa had earlier met with Modi in New Delhi after he traveled to India to attend his swearing-in ceremony.
Rajapaksa gave his support in writing to the Yoga initiative which would need to be ratified by the UN General Assembly by September 2015 for coming into effect.
Koirala and Hasina also promised their full support to Modi's suggestion to the UN to celebrate International Yoga Day once a year, which he made during his 35-minute speech at the UN General Assembly.