He's likely to use his interactions with American officials to halt a rapid deterioration in US-Pakistan relations, reports said.
Speaking to Geo News, Abbasi said: "Pakistan has made clear its national policy to America".
Pakistan Prime Minister Shahid Khaqan Abbasi arrived in NY on Tuesday to attend the 72nd session of the United Nations General Assembly (UNGA), where he is expected to raise the Kashmir issue.
VIDEO: Abbasi's predecessor was Nawaz Sharif, who suffered a major blow yesterday when Pakistan's Supreme Court dismissed a petition seeking a review of the decision that disqualified him.
He also said that the government is not satisfied with the ongoing accountability drive.
Abbasi will meet US Vice President Mike Pence in NY at the United Nations headquarters later on Tuesday, the White House said.
Ambassador Maleeha Lodhi said nine bilateral meetings, including with US Vice President Mike Pence, have been confirmed and more could also take place as the prime minister's visit proceeds.
Ex-minister went on to complain that such remarks weaken Pakistan s stance in the global level. It is entitled: "The responsibility to protect and the prevention of genocide, war crimes, ethnic cleansing and crimes against humanity".
Other meetings will be with the Jordanian King and leaders of Turkey, Afghanistan, Sri Lanka, Iran, the United Kingdom and Nepal.
The two leaders discussed internal party issues and the domestic political scenario in the meeting. He will outline Pakistan's positions on key global political, social and development issues of vital concern to the country.
The Prime Minister House of Pakistan in a statement said "The remarks are simply baseless and have no reference to discussions with any media person".
In response to reports of Abbasi's meeting with Pence, Rabbani said, "I suggest the prime minister not to meet the U.S. vice president".