While Ramesh shared a poem critical of the Scindia family, the Union minister told the Congress leader to study history more than poetry.
In recent days, there have been complaints from passengers about long queues and waiting hours at the airport.
The Bharatiya Janata Party leader attacked the Congress for according Rahul Gandhi a "special treatment" following his conviction in a defamation case and accused the party of pressuring the judiciary, and doing everything possible to stay relevant.
The BJP lost 15 of the 80 Lok Sabha seats in 2019. Union ministers have been deployed in all 15, tasked with turning the result around.
This visit by the prime minister comes weeks ahead of the 'pran pratishtha' or consecration ceremony of the Ram temple.
Tirumurti voiced deep concern for the safety and security of thousands of Indian citizens, including students, stranded in Ukraine.