The BJP hit back with its President and Union Home Minister Amit Shah leading the attack.
He referred to Congress interim president Sonia Gandhi's foreign origins, saying the leaders of the grand old party were more aware of the "culture of Italy than India".
"Kharge saheb said that what was the need of doing drama by worshipping Rafale. You tell whether you should do arms worship to conquer the enemy on the day of Vijayadashami or not?," Shah asked while addressing a rally in Kaithal of Haryana.
"It is not Kharge's fault in this, he is more aware of the culture of Italy than India," he added.
Shah said the sole purpose of Congress was to oppose the BJP and added that the puja was performed by the Defence Minister as per Indian traditions.
"Defence Minister Rajnath Singh performed Shastra puja of Rafale yesterday [Tuesday] in France. Congress did not like it. Is Shastra Pujan not performed on Vijayadashami? They should ponder over what needs to be criticised and what not," he said.
He said that 'Shastra Puja' is done on Vijayadashami which symbolises the victory of good over evil.
The Home Minister congratulated Prime Minister Narendra Modi and Rajnath Singh over India getting its first Rafale fighter jet and said it will strengthen the country's security.
"Defence Minister Rajnath Singh performed 'Shastra Puja' of Rafale yesterday in France. But Congress leaders are opposing even this. Is 'Shastra Puja' not performed on Vijayadashami? I want to them to think about what should be opposed and whatnot," he said.
Kharge had said that Congress-led government procured arms without indulging in show off.
"There is no need to do such 'tamasha' (drama). When we bought weapons-like the Bofors gun previously purchased, no one went and brought them while showing off," Kharge said.
"Our Air Force officers judge whether they are good or not. These people go, show off, sit inside (the aircraft)," he added.
Congress leader Sandeep Dixit had on Dussehra hit out at BJP and asked why the Defence Minister, and not the defence forces, had received the fighter jet in France.
However, disgruntled Congress leader Sanjay Nirupam said that the ceremony was an Indian tradition.
Nirupam termed Kharge and atheist and said that people like him do not represent the party's view.
"'Shastra puja' cannot be called a tamasha. There has been an old tradition of 'Shastra puja' in our country. The problem is that Kharge Ji (Congress leader Mallikarjun Kharge) is an atheist. In the Congress party, not everyone is an atheist," he said.
Rafale was a major poll plank of Congress during 2019 Lok Sabha polls with the party raising questions on the deal signed by the Modi government to replace the deal being negotiated by the UPA government .
Singh performed Shastra Puja (worship of weapons) on Dussehra after receiving the first of the 36 Rafale jets in the French port city of Bordeaux on Tuesday. He wrote "Om" on the jet and placed lemons before it as part of the rituals.
The first of the 36 French-built Rafale fighter jet bearing the tail number RB-001 was formally handed over to India on Tuesday. The ceremony coincided with the foundation ceremony of the IAF.