Pavinya Nithiyakumar, aged 19 months, and Nigish Nithiyakumar, three, were found suffering from knife wounds at a house in Aldborough Road North, Ilford, on Sunday.
The 40-year-old man was arrested at a London hospital, where he is currently receiving treatment and remains under police guard.
He was previously described as being in a critical condition, but there have been no further updates on his health.
Police were called to the home at 5.30pm on Sunday to reports of a man and two children having been injured.
Pavinya was pronounced dead at the scene, while Nigish died later in hospital.
Scotland Yard said all those involved were “known to each other” and that they are not looking for any other suspects.
The children’s family have been informed and their mother is being supported by specially trained officers.
Detective Chief Inspector Vicky Tunstall, from the Metropolitan Police, described the deaths as “extraordinarily tragic” and urged anyone with information to come forward.
Any witnesses or anyone with any information is asked to call police on 101 or contact via Twitter @MetCC, quoting CAD 5669/26 APR.
To give information anonymously contact Crimestoppers on 0800 555 111 or online at crimestoppers-uk.org.