Parameshwara, a senior Congress leader, accused the BJP MP of arranging the aircraft to ferry its party MLAs, a charge denied by the saffron party leader.
"Traces of BJP's role in destabilizing the government are all over the place. It is disgraceful that the party is attempting to topple a democratically elected government and grab power through the back door when the state is reeling under one of the worst droughts," Parameshwara tweeted.
He attached a report which said that the aircraft used to fly the rebel Congress and JD-S MLAs from Karnataka to Mumbai belonged to a company linked to the BJP MP.
Chandrasekhar responded that the aircraft was a commercial one that it had been chartered even by Congress Ministers in the past.
"So don't blame me or an 'aircraft' or BJP for the problems in your crooked corrupt opportunistic alliance," the BJP MP said.
The verbal spat came at a time when the beleaguered ruling JD-S-Congress alliance in Karnataka was on the brink on Monday after Small-Scale Industries Minister H. Nagesh resigned and withdrew support to the 13-month-old coalition government.
On Saturday, over a dozen Congress and JD-S MLAs resigned. The Congress accused the Bharatiya Janata Party (BJP) of hatching a conspiracy to topple the coalition government.
( With inputs from IANS )