Here are 10 developments in the story:
Sushma Swaraj, who met Prime Minister Narendra Modi on Sunday, has defended her decision. She said she had backed Lalit Modi's request last July for travel documents from the British government on "humanitarian grounds" so that he could be with his wife who needed surgery for cancer in Portugal.
The opposition has alleged conflict of interest. Sushma Swaraj's husband Swaraj Kaushal was Lalit Modi's lawyer for 22 years and her daughter Bansuri has been his lawyer for seven years. The Congress has said Ms Swaraj should resign on moral grounds.
Lalit Modi was removed as chairman of the multi-billion dollar Indian Premier League (IPL) in 2010 over allegations of corruption for which he is being investigated. Indian authorities revoked his passport but it was restored in August last year by the Delhi High Court.
In a series of tweets, Sushma Swaraj has asserted that she has done nothing wrong. "What benefit did I pass on to Lalit Modi... He was in London. After his wife's surgery, he came back to London. What is it that I changed?"
Ms Swaraj said Lalit Modi told her in July last that he had to sign the consent papers for his wife's operation on August 4 in Portugal. However, the law in Portugal does not require written consent, the opposition says.
Reacting to the controversy, Lalit Modi said on Sunday, "Waiting and watching the story unfold. No comment for now."
According to the British media, Indian-origin British MP Keith Vaz used Sushma Swaraj's name to put pressure on UK immigration officials to grant travel papers to Lalit Modi.
Sushma Swaraj claimed Lalit Modi had said that the British government was ready to grant him the papers, but was restrained by a communication from the previous Congress-led government that it would "spoil Indo-UK relations."
"Taking a humanitarian view, I conveyed to the British High Commissioner that the British Government should examine the request of Lalit Modi as per British rules... If the British Government chooses to give travel documents... that would not spoil our bilateral relations," Ms Swaraj said.
The ruling BJP has rallied around the foreign minister. BJP President Amit Shah said, "There were no moral grounds involved. The help was based on humanitarian grounds." Home Minister Rajnath Singh said, "What Sushma ji has done, it is right... I want to clarify that the government stands with her."
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