"Building on the mutual desire for peace between our two countries, I wish to propose a meeting between Foreign Minister Qureshi and External Affairs Minister Swaraj, before the informal meeting of the SAARC Foreign Ministers on the sidelines of the UN General Assembly in NY", he said in the letter, seeking resumption of the dialogue process started by his predecessor Nawaz Sharif.
The meeting was scheduled to take place in NY later this month on the sidelines of UN General Assembly session.
Announcing the cancellation of the meeting, External Affairs Ministry Spokesperson Raveesh Kumar said the incidents "exposed" the "true face" of Pakistan's new Prime Minister Imran Khan to the world as well as Islamabad's evil agenda behind the proposal for talks.
"Some elements don't want a resumption of talks between India and Pakistan", Mr Qureshi told SAMAA TV.
The Indian government's acceptance of Pakistani Prime Minister Imran Khan's proposal - that the two countries' foreign ministers meet on the sidelines of the United Nations General Assembly (UNGA) session next week - has sparked an optimistic debate in the Press and social media.
In response, India sent elite soldiers into Pakistan territory to destroy what it said were militant staging grounds, and Modi called Pakistan a "mothership of terrorism".
The India-Pakistan ties nose-dived in recent years following a spate of terror attacks in India by Pakistan-based terror groups.
In his letter, Khan said that it was important to "peacefully resolve all outstanding issues, including the Jammu and Kashmir dispute, to bridge differences and achieve a mutually beneficial outcome".
Pakistani and Indian flags are seen during a daily flag-lowering ceremony at the Wagah border, some 20 kilometres (12 miles) east of Lahore, Pakistan, December 14, 2006.
India's foreign ministry, however, said the NY meeting between Swaraj and Qureshi did not represent a shift in New Delhi's relations with Islamabad.
Khan, a former cricketer turned politician, peppered his campaign speeches with anti-India rhetoric but reached out to Delhi in the first days of his leadership to propose the meeting.
Observers are sceptical if the two countries will be able to resume full spectrum of dialogue given the parliamentary elections in India next year. Khan has now in his letter asked for peace talks by calling for the resumption of the comprehensive dialogue process between the two countries.