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In a case that has become an election-year political embarrassment for the ruling Congress party, Tharoor's wife was found dead in a luxury hotel room in New Delhi after sending tweets that suggested her husband was having an affair with a Pakistan-based journalist.
An autopsy found that Sunanda Pushkar's death was "sudden and unnatural" and that her body bore injury marks, although doctors said this did not mean the injuries had caused her death.
Tharoor, a high-flying former U.N. diplomat, called for a quick investigation into the death of his wife, saying he hoped this would put an end to rumours about their personal lives.
"I have finally had a chance to catch up with media reports and am horrified to read the reckless speculation rampant there," Tharoor, a junior human resource development minister, wrote in a letter to Home Minister Sushil Kumar Shinde.
"I pledge my full and unstinting cooperation. Nothing short of truth will end the indignity to which my wife and I are being subjected."
Later on Sunday, Tharoor, 57, gave his testimony to subdivisional magistrate Alok Sharma, who is leading the inquest into the death of his wife.
There was no word on what he had told the magistrate and he drove away without making any comment to reporters gathered outside the office, his face drawn.
The scandal has erupted just as the Congress party, led by Rahul Gandhi, is preparing to fight a tough election against a resurgent main opposition party as well as a new political group that promises clean and open politics.
Rivals have painted Congress as a party of power and patronage, engulfed in corruption scandals and unable to hold its leaders to account for their actions.
Tharoor's marital problems have been splashed across the front pages of newspapers and pored over by 24-hour television channels, prompting calls by the opposition for a fuller inquiry into the death of his wife.
"The circumstances of this case are such that we need to get to the bottom of this," said Subramaniam Swamy, a leader of the opposition Bharatiya Janata Party.
Politicians in India have traditionally refrained from attacking each other's personal lives and sex scandals involving top leaders are rare.
Tharoor and his 52-year-old wife hit the headlines last week when she said she had gone into his Twitter account and posted what she said were intimate messages from Pakistani journalist Mehr Tarar to expose a "rip-roaring affair".
Tarar hit back saying she would sue Sunanda for calling her a Pakistani spy and denied having an affair with Tharoor. She said she was friends with Tharoor on Twitter and exchanged comments about articles she had written, but that was all.
Five members of Tharoor's staff were also questioned by the magistrate leading the inquest into the death of Sunanda. Under Indian criminal law, a magistrate must conduct an inquiry if a woman has died within seven years of marriage.
The Tharoors married in late 2010, the third marriage for both.
A Delhi police spokesman declined to comment on the possible lines of inquiry before a final post-mortem report had been issued.