Gilani made the remarks while taking the leadership of all political forces "into confidence on the dialogue process with India", an official statement said.
Khar "would be able to put across Pakistan's perspective with confidence", he said.
34-year-old Khar, Pakistan's youngest and first woman Foreign Minister, travelled to New Delhi to hold talks with her Indian counterpart S M Krishna on Wednesday, Jul 27.
The ministerial meeting will review talks held in recent months by secretaries of the two countries on a wide array of issues, ranging from commerce to counter-terrorism.
Gilani talked to top political leader on phone to take them into confidence on the Pakistan-India talks. He informed them of the agenda of the talks and progress in deliberations in various sectors.
"The dialogue would cover all aspects and issues between the two countries, including the core issue of Jammu and Kashmir," he said.
Khar is leading the Pakistani delegation, which includes Foreign Secretary Salman Bashir and other officials from the Foreign Ministry.
The political leaders expressed confidence and extended complete support to the Pakistan delegation, the statement said.
Among the leaders contacted by Gilani were PML-N chief Nawaz Sharif, Pakistan Tehrik-e-Insaf party head Imran Khan, Maulana Fazlur Rehman of the Jamiat Ulema-e-Islam, PML-Q president Chaudhry Shujaat Hussain and MQM leader Ishrat-ul-Ebad, who is the Governor of Sindh.