Pavinya Nithiyakumar, aged 19 months, and Nigish Nithiyakumar, three, were found with knife wounds at their home in Aldborough Road North, Ilford, after officers were called at about 5.30pm on Sunday.
Pavinya was pronounced dead at the scene and Nigish died later in hospital.
Officers also found a 40-year-old man with a knife injury. He was in a critical condition in hospital, where police are present.
All those involved were “known to each other”, Scotland Yard said.
It added that “at this early stage, police are not currently looking for anyone else in connection with this incident”.
No formal arrest has been made.
The children’s next of kin have been informed and their mother is being supported by specially trained officers.
“The ending of these innocent young lives is extraordinarily tragic and we are working hard to fully understand what may have caused this to happen,” said Detective Chief Inspector Vicky Tunstall.
“Whilst I know the effects of this crime are reverberating throughout the local community, please be reassured that we are not seeking any other person(s) in connection with the deaths and there is no cause for the community to be fearful or alarmed.”
Anyone with information should call 101 or tweet @MetCC, quoting CAD 5669/26 APR.
Alternatively, people can contact Crimestoppers, anonymously, on 0800 555 111.