Koirala cancelled his visit to hold talks with the Madhesi and other regional groups opposed to the Constitution adopted on Sunday.
Madhesis are Indian-origin people living on the foothills of Nepal's Terai region.
The cancellation of the visit comes two days after India expressed concern over the violence in Terai districts and asked the government to resolve the issue politically through peaceful means of dialogue instead of using force.
"I have to lead the Nepalese delegation to New York, as Prime Minister Koirala has important task of holding talks with the agitating Madhesi parties at home," Singh told PTI before flying to the US.
Foreign Minister Mahendra Bahadur Pandey and other officials of the Ministry of Foreign Affairs included in the delegation.
The Madhesi parties are opposed to the new Constitution adopted through the Constituent Assembly.
More than 40 people have died in southern and western Nepal where Madhesi parties and Tharu ethnic groups have been protesting for more than a month over splitting the country into seven provinces.
The escalating violence has raised concerns in India, which had it "repeatedly cautioned the political leadership of Nepal to take urgent steps to defuse the tension in these regions."
"We still hope that initiatives will be taken by Nepal's leadership to effectively and credibly address the causes underlying the present state of confrontation," the External Affairs Ministry in New Delhi had said in a statement.