A 17-YEAR-OLD girl has been shot dead by a man, allegedly after objecting to his urinating near her home in New Delhi.

The man also reportedly shot the girl's mother in the incident, in the Nizamuddin area late on Wednesday.

Police began investigating after a complaint was filed the following day and said overnight they would soon arrest the accused, a former tenant in the building where the family lives.

"The man ... was relieving himself at the staircase leading to the house, when the girl and her mother objected and shouted at him to leave," area police chief Sunil Kumar said.

"An angry argument followed, after which the man left. He returned to the girl's apartment with a pistol sometime later and shot them," Mr Kumar said.

Mr Kumar said the "sudden provocation" resulting from the argument had led to the murder.

Nearly half of India's 1.2 billion people do not have toilets at home and many people urinate or defecate in the open.