Both parties retained the seats in Rajasthan that fell vacant after the death of their MLAs last year.
Gehlot had isolated himself on Wednesday after his wife Sunita Gehlot tested positive for coronavirus.
Even though the BJP has rejected the charge, things do not seem to be smooth after rebellion by a section of Congress led by then Deputy CM and Rajasthan Congress unit chief Sachin Pilot in July this year.
Vaishnav's family members had demanded action against the Station House Officer, an investigation by a senior-rank official, compensation and government job to a family member.
Congress chief Sonia Gandhi also set up a three-member committee to resolve the issues raised by party rebels in Rajasthan.
The session comes after a month-long political crisis in the state which started with the rebellion by Sachin Pilot and 18 other Congress MLAs.
The Congress on Thursday revoked the suspension of Bhanwarlal Sharma and Vishvendra Singh, two MLAs who had rebelled against the Ashok Gehlot government.
In an apparent reference to the return of Sachin Pilot and other rebel MLAs, the chief minister said that he told the MLAs on Tuesday night that they have to bear and work in the interest of people.
On his return, after a month of political uncertainties in the desert state, Pilot is most likely to be accommodated in the national leadership, sources aware of the talks between the party top brass and the leader said.
After the meeting with Rahul Gandhi and Priyanka Gandhi, the party said Pilot will work in the interest of the Congress and its government in Rajasthan.