According to Foreign Minister Shah Mehmood Qureshi, who is accompanying Khan on the trip, Khalilzad in the meeting on Sunday shared with the Prime Minister "how far his negotiations with the Taliban had gone, the nature of the talks and what expectations he holds in the future", Dawn news reported.
"So he (Khalilzad) presented his entire analysis of the US-Taliban talks," Qureshi added while briefing the media about Khan's meetings.
Qureshi also briefed the press about the Prime Minister's other engagements for the day and the delegation's efforts to raise the issue of Kashmir with various international human rights organisations, including Amnesty International and the International Red Cross.
The Foreign Minister also spoke of the Prime Minister's meeting with Graham, who he said was one of four Senators who had written to US President Donald Trump to call to his attention the "worrying situation" in Kashmir.
"We thanked him (Graham) for taking on the responsibility to raise his voice for the unarmed Kashmiris...," Qureshi said, adding that the visiting Pakistani delegation had requested Senator Graham to continue to raise his voice and told him that US Congress can play an important role in this.
He said that the premier also met George Soros, the philanthropist behind the Open Society Foundation (OSF), reports Dawn news.
Earlier on Sunday, Khan met Amnesty International Secretary-General Kumi Naidoo and discussed the Kashmir issue.
He also held talks with the founder of Kashmir Study Group, Farooq Kathwari, on the prevailing situation in Jammu and Kashmir.
Khan reached New York on Saturday where he will address the 74th session of the UN General Assembly (UNGA) on September 27, which would focus on Pakistan's perspective and position on the Jammu and Kashmir issue and on its current human rights and related dimensions.
He will meet Trump, UK Prime Minister Boris Johnson and China's Vice President Wang Qishan on Monday.
( With inputs from IANS )