A 23-year-old woman was allegedly killed with an iron rod by a man in south Delhi's Malviya Nagar area on Friday for turning down his marriage proposal, police said.

The victim and accused were first cousins, with their mothers as sisters, they said.

The victim, identified as Nargis, was attacked by a 28-year-old Irfan when she was with him in a park near Delhi University's Sri Aurobindo College, police said, adding, the accused has been arrested.

Delhi Chief Minister Arvind Kejriwal tweeted slamming the state of law and order in the city and urged the Union Home Minister and the Lieutenant Governor to take strict measures in that direction.

"Another daughter was brutally murdered in Delhi, it is very sad. Law and order has become a serious issue in Delhi. It is a request to the LG and the Home Minister, make the police a little active. The safety of the daughters of Delhi and the people of Delhi is very important," he said.

Police said they got the information at 12.08 pm that a man hit a woman in her head in the Vijay Mandal Park in Shivalik A Block of Malviya Nagar and fled.

The woman's body was found under a bench with her head bleeding and an iron rod lying near her, Deputy Commissioner of Police (south) Chandan Chowdhary said.

According to police, Nargis and Irfan were in a relationship earlier and there were also talks about their marriage, but Nargis's family finally disapproved of it.

Nargis stopped talking to Irfan, which made him even more agitated, police said.

Nargis had completed her graduation this year and used to attend coaching classes in Malviya Nagar, they said.

The Delhi Commission for Women has issued a notice to police seeking details of the murder.

The notice issued by the DCW chairperson Swati Maliwal sought details of the FIR registered in the matter and arrested accused and any other action taken from the Deputy Commissioner of Police (South) by July 31.