During her week-long stay, Ms Swaraj, leading a high-powered Indian delegation, is expected to hold about 20 bilateral and trilateral meetings with leaders attending the session.
Ms Swaraj, was received at the airport by the Indian Ambassador to the US Navtej Sarna, and India's permanent Representative to the United Nations Syed Akbaruddin.
She would kick off her official engagement later today with a trilateral meeting with her American and Japanese counterparts Rex Tillerson, and Taro Kono respectively.
Aimed at lending momentum to cooperation between the three countries, the meeting also turns significant amid China flexing its muscles in the region.
In a day jam-packed with consecutive meetings, Ms Swaraj will also participate in a high-level meeting on UN reforms, hosted by the US and chaired by president Donald Trump.
India is among the 120 countries who have supported the reform efforts of the UN Secretary General.
India has said that the UN reforms need to be "broad- based and all-encompassing" and the changes should not be restricted to its Secretariat only.
Ms Swaraj will also participate in a special panel of selected countries by the UN Secretary General on climate action, he said earlier.
She will address the UNGA on September 23.
The minister is scheduled to have a series of meetings today including that with Tunisian Foreign Minister Khemaies Jhinaoui, Bhutanese Prime Minister Tshering Tobgay, Danish Foreign Minister Anders Samuelsen, Latvian Foreign Minister Edgars Rinkevics and her Bolivian counterpart Fernando Huanacuni Mamani.
Mr Akbaruddin in an interaction with Indian reporters ruled out a bilateral meeting between Swaraj and her Pakistani counterpart.
However, the two leaders are likely to see each other during several multilateral meetings including that of SAARC and the Shanghai Cooperation Organisation (SCO).
Ms Swaraj is scheduled to leave for India, a day after her address to the UN General Assembly.
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