Vijayan made the request in a letter to Jaishankar in this regard, a statement from the chief minister's office said here.
Jaishankar was briefing members of the Consultative Committee on External Affairs including former Congress president Rahul Gandhi.
It said the two sides also deliberated on the Iran nuclear deal of 2015, known as the Joint Comprehensive Plan of Action (JCPOA), from which the US pulled out in 2018.
India decided to stay away from the trade deal after years of negotiations failed to bring out a solution to New Delhi’s concerns.
India said the proposed pact in its current form would have adverse impact on lives and livelihoods of all Indians.
Ties between China and India nosedived after the 73-day confrontation between militaries of the two countries in Doklam in 2017.
In remarks that come at a time several countries have called for a greater Indian role in the Indo-Pacific, the minister also said it is not the India way to be mercantilist.
External Affairs Minister S Jaishankar on Tuesday said India had been largely successful in creating own platforms, organising discourses and shaping narratives.
The SCO secretary general is in Delhi on a four-day visit to attend the Raisina Dialogue.
Foreign Minister held discussions over regional issues with his Jordanian and Qatari counterparts Ayman Safadi and Mohammed bin Abdulrahman Al Thani respectively.
Jaishankar defends NDA government's decision to allow ISI officials to visit Pathankot airbase in 2016
Jaishankar appeared to be critical of past government for not making adequate attempts to find solution to long-pending problems.
After the violence in JNU campus, Jaishankar, a JNU alumnus, had swiftly condemned the incident, saying it is completely against the tradition.
The SAD also asked Dr Jaishankar to seek a categorical assurance from Pakistan PM Imran Khan that assets and lives of minorities would be protected.
Jaishankar said he had a conversation with Zarif and asserted that India remains deeply concerned about the levels of tension in the region.
The JNU administration said "masked miscreants armed with sticks were roaming around, damaging property and attacking people".