The specifics: Vijay Veer allegedly killed his wife Suman in the incident that occurred at a housing society called Indira Enclave in Delhi's Neb Sarai on Thursday, 27 April, according to the Delhi Police.
Devika and Shashank, the two children aged 30 and 28, suffered injuries and have been hospitalised.
A case has been registered under Sections 302 (Punishment for murder) and 307 (Attempt to murder) of the Indian Penal Code against Vijay Veer, who hails from UP's Garh Mukteshwar.
Further investigation is ongoing, police said.
"The accused in order to eliminate his family attacked his wife with axe while she was sleeping. After murdering his wife, he went inside the room of his kids and attacked them with an axe," Delhi Police said.
At the scene: Police said that they found the wife laying on the bed in a pool of blood with multiple injuries on her neck.
The accused had also tried to injure himself and has been shifted to a hospital, the police further said.
Backstory: A father of two, Vijay Veer was reportedly a builder.
Delhi Police alleged that he had extramarital affairs and would assault his wife when she objected.
"Both children used to support their mother and on this, he had grudges on them," police said.
Of note: Veer had been arrested six years ago for allegedly shooting at his family after a quarrel arose.
His son had suffered gunshot injuries and a case was registered at Mehrauli Police Station.
However, the case was later quashed after the family chose to settle the matter out of court.