"Not yet certain whether Sunanda Pushkar's death was suicide or murder," Congress spokesman Abhishek Singhvi said in Delhi.
That much was clear from what Delhi Police chief BS Bassi told the media, he said.
Mr Bassi today said Sunanda Pushkar was poisoned to death, but whether the poison was administered orally or injected into her body was still under investigation.
In light of the latest revelation, Mr Singhvi appealed for maintaining a sense of balance while refraining from giving it any sensational overtone.
He said the FIR was "just a beginning and not an end of a legal process".
"As police have also said it's not at all clear that whether it's a self-administered poison or outside-administered poison... every person has the full right to be treated as completely innocent unless and until a process of law goes beyond and further," the Congress leader added.
Mr Tharoor was minister of state for human resource development in the Manmohan Singh government at the time his wife was found dead under mysterious circumstances at the Leela Palace hotel in New Delhi January 17, 2014.