In a statement, Rajesh said Sunanda Pushkar was one of the strongest personalities and to even remotely think that she would do any bodily harm to herself is "preposterous" and "should not be believed".
He also sought speedy investigation into the case "to put an end to the rumours that are hurting" the family. The probe into the high-profile case was transferred to the Crime Branch on Thursday considering its "sensitive nature" and "complexities" involved.
"I have been with both Shashi Tharoor and my sister throughout their journey together and can say with utmost confidence that they were a couple madly in love with each other. Differences, if any, were momentary and do happen in every household, and we do not believe that they have any bearing on the incident," he said.
Rejecting speculation in the media about Sunanda Pushkar's death, he said both he and his father were "deeply disturbed" at the "slanderous statements" that have been made in the media regarding her death.
"I have known my sister to be an angel at heart but to often impulsively say things she did not mean and withdraw them later."
Sunanda Pushkar, 52, was found dead in a 5-star hotel in South Delhi on January 17 night, a day after her Twitter spat with Pakistani journalist Mehr Tarar over an alleged affair with Shashi Tharoor.
"My sister was one of the strongest personalities and to even remotely think that she would do any bodily harm to herself is preposterous and should not be believed. Also to think that my brother-in-law would do any harm to her is unimaginable," he said.
He requested that the matter be put to rest so that peace can be bestowed on the departed soul.
This was the second statement issued by a family member of Sunanda Pushkar.
Earlier this week, Sunanda's 21-year-old son from a previous marriage, Shiv Menon, had released a statement to the media saying his mother was "too strong" to commit suicide and she died due to an "unfortunate combination of media stress, tensions and a wrong mix of different medication".
He asserted that he did not believe that there was a foul play in his mother's death, saying both Shashi Tharoor and his mother were "very much in love" despite their "occasional differences" and that he did not believe the Union minister was capable of harming her physically.
On Tuesday, a sub-divisional magistrate, who probed the case, had directed Delhi Police to investigate the murder or suicide angles in the case while concluding that "poisoning" was the cause of her death.
The autopsy report had mentioned more than a dozen injury marks on Sunanda Pushkar's body besides a "deep teeth bite" on the edge of her left palm.
The Crime Branch team probing the case has decided to go for advanced forensic tests to determine cause of injuries on her body.
The autopsy report had mentioned use of blunt force for the injury marks on both her hands and left cheek.