State Congress president Bharatsinh Solanki hit back at Mr Rupani, calling him "a Chief Minister by chance".
Addressing party workers at the Sabarmati Riverfront in Ahmedabad, Rahul Gandhi said on Monday that only genuine party workers who have fought against the BJP and its ideological parent RSS will get tickets and not those who "parachuted" into the party recently.
Taking a dig at the Congress vice president, Mr Rupani said, "Rahul Gandhi asserted his party will not give tickets to those who parachuted into the party recently. I am surprised because he himself landed in his party by parachute. Rahul Gandhi was made the leader of the party because of his Nehru-Gandhi lineage".
Addressing reporters in Gandhinagar, Mr Rupani said even Congress workers would acknowledge that Rahul Gandhi was "imposed" on them despite not having any "ground connect".
"Rahul Gandhi has been projected as the leader by (Congress president) Sonia Gandhi out of her blind love for her son. Otherwise, he does not have any ground connect. And still he is talking about the parachute system. Even Congress workers know this reality," the chief minister said.
Reacting to Mr Rupani's jibe, Mr Solanki said the BJP leader became chief minister only "by chance". "Vijaybhai is not aware of either geography or history. Nehru-Gandhi family is one of those rare families in the world that sacrificed themselves for their country. Indiraji and Rajivji gave their lives to keep this country united," Mr Solanki said.
"As far as the parachute system is concerned, I want to remind Vijaybhai that Rahulji is very much connected with people. His election to the Lok Sabha from Amethi in 2004, 2009 and 2014 reflects that," he added.