The genesis of the controversy was disclosure of emails showing that she had spoken to Indian-origin British MP Keith Vaz and its High Commissioner here James Bevan favouring the grant of travel documents to Lalit Modi to go to Portugal, purportedly for his wife's cancer treatment in June last year.
Modi, who is wanted in India, has made London his home since 2010 to avoid a probe for alleged foreign exchange regulation violations in the T20 cricket tournament held in South Africa in 2009.
The previous UPA government had revoked his passport and had pressed for his extradition.
According to British media which quoted leaked emails, Vaz cited Swaraj's name to put pressure on UK's top immigration official to grant British travel papers to Lalit Modi, who subsequently got the documents in less than 24 hours.
Vaz also offered to help Swaraj's nephew Jyotirmay Kaushal to apply for a British law degree course, the report said.
After the reports surfaced, 63-year-old Swaraj said in a series of tweets that she had taken a "humanitarian view" and conveyed to the British high commissioner that they should examine Modi's request as per their rules and "if the British government chooses to give travel documents to Lalit Modi -- that will not spoil our bilateral relations".
Facing opposition attack, Swaraj said, "What benefit did I pass on to Lalit Modi -- that he could sign consent papers for surgery of his wife suffering from cancer? He was in London. After his wife's surgery, he came back to London. What is it that I changed?"
She also reportedly spoke to Prime Minister Narendra Modi explaining her position on the issue.
Opposition parties demanded her resignation, alleging grave impropriety on her part in helping a fugitive from law. Congress questioned even the role of the prime minister as to whether her action had his "tacit" endorsement.
Contending that the prime minister's role was under a "cloud of suspicion", Congress posed 11 questions to him, including "what happens to transparency and non-corruption" promise made by him.
However, the government, the BJP as well as the Rashtriya Swayamsevak Sangh, strongly "justified" Swaraj's action and rejected resignation demands. Home Minister Rajnath Singh and BJP chief Amit Shah asserted that she had done no wrong and only acted on "humanitarian" grounds.
The government support was expressed after Home Minister Rajnath Singh met the prime minister.