He has also hit out at Prime Minister Narendra Modi for praising chief ministers of Madhya Pradesh and Rajasthan while remaining silent on their "illegal" acts.
The Congress vice president attacked Swaraj for being "secretly" kind and charitable to Lalit Modi, whom he termed as a criminal, and asked her to tell the country how much money she and her family "have received" in their bank accounts from the former IPL chief.
"We also agree that Parliament must function. But, we have raised a basic issue. We have said, and I have said it three times, Sushma Swarajji, the chief minister of Rajasthan and the chief minister of Madhya Pradesh have carried out in some cases illegal acts. In Madhya Pradesh, there are murders happening and our prime minister does not feel it necessary to comment on them.
"He praises the chief ministers. He completely ignores the fact that the future of thousands of people in Madhya Pradesh has been destroyed by his chief minister. He completely ignores the fact that there is a business relationship between a criminal and his chief minister of Rajasthan," Rahul said as the logjam in Parliament continued over protests by Congress.
At a rally in Gaya on Sunday, Modi had said Madhya Pradesh and Rajasthan have come out of BIMARU category under BJP chief ministers and were moving fast on the path of development.
Targeting External Affairs Minister Swaraj, Rahul said it "was nice to hear her speech in Parliament about how one should be very kind to Lalit Modi and should be charitable to him".
"You want to be kind, you want to be charitable, why do it in secret. Why hide, why not tell your whole ministry, why not tell the whole country you are doing it," he said.
The Congress vice president said he has asked a specific question to Swaraj that there are financial transfers that have taken place between Lalit Modi, who is a criminal wanted by different agencies, and her family.
"Please explain to the country and the people of India, how much money of Lalit Modi has come into your bank account and that of your family. Please simply disclose this and the House will function," he said.
Asked if Congress was isolated in Parliament due to its protests, he said, "We are not isolated".
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