Khar was addressing the 193-member UN body on behalf of Prime Minister Yousuf Raza Gilani who could not attend the 66th session due to floods in Pakistan.
The 34-year old Foreign Minister said Pakistan is reaching out to its "immediate neighbours" with a "sincere" desire to join hands and bring about "durable peace and development, by a win-win approach.
"I am happy to note that both Pakistan and India are now engaged in a substantive dialogue process.
A dialogue process that we in Pakistan hope will be uninterrupted and uninterruptable.
We certainly intend to make this engagement fruitful and premise it on the promise of a mutually rewarding enterprise that would enable us to optimally avail the complementarities that exist," she said in her maiden speech.
Khar said Pakistan looks forward to "resolving all outstanding issues including Kashmir," which is among the oldest on the United Nations agenda and has been the subject of several Security Council resolutions.
"A peaceful resolution that accords fully with the aspirations of the Kashmiris is indispensable for durable stability as is the need for safeguarding of their fundamental human rights," she said, adding that Pakistan will "support" the human rights of Kashmiris. .