Mr Singh was expelled from the Samajawadi Party in 2010.
Politician Amar Singh was interrogated in Delhi today in connection with the murder investigation of Sunanda Pushkar, who was married to Congressman Shashi Tharoor.
Ms Pushkar, 51, was found dead in a five-star hotel in Delhi a year ago. Mr Singh, 59, told a private television channel recently that she had broken down and told him that she wanted to reveal information about the Indian Premier League or IPL, the hugely-popular twenty-20 cricket league.
He said days before Ms Pushkar died, he dined with her and Mr Tharoor at Delhi's famous Bukhara restaurant and that she "started crying and said 'I have nothing to do with IPL'.
"Mr Singh claims that Ms Pushkar told him that she "took the entire blame" for "this man's wrongdoing for the sake of my love and affection for him".
In 2010, Mr Tharoor was forced to quit as Union minister in the Congress-led government after it emerged that Ms Pushkar, whom he had not yet married, had been gifted equity worth nearly Rs 70 crore in the Kerala franchise of the IPL. There were allegations that she had served as a front for an illicit payment to Mr Tharoor.
"Shashi Tharoor is a good friend. I'm not against him. I wish that the truth comes out," Mr Singh said after the questioning. The police, he said, had lodged a murder case and it was up to them to prove it.
Mr Singh was expelled from the Samajawadi Party in 2010.
Delhi Police Chief BS Bassi said the police will question Mr Tharoor again as they had not been able to get all the information during his questioning on January 19. Ms Pushkar's son Shiv Menon will also be called for questioning, he said.
Mr Bassi has been stressing that the IPL angle will be explored thoroughly in the inquiry.
The police registered a murder case for Ms Pushkar earlier this month. Before that, her death had been debated as an accidental overdose or a possible suicide.
Mr Tharoor has said he is "stunned" that the police believes that Ms Pushkar was killed.
Days before she died, Ms Pushkar had publicly accused him of having an affair with a Pakistani journalist.