Payal, who has been residing at 7, Akbar Road bungalow since 1999, however, refused to move out and urged the court to pass an order.
The court then said a detailed order will be passed with regard to the time within which she and her children will have to vacate the bungalow.
"Will you gracefully evict or I should pass an order?" Justice Indermeet Kaur asked Payal's counsel, who categorically stated that the court should pass the order.
The judge also noted that Delhi Police will provide security to Payal and her children, who are 'Z' and 'Z plus' security protectees, during their stay in the capital.
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The high court was hearing Payal's plea seeking that she and her children be not evicted from 7, Akbar Road (type VIII) bungalow here or an alternative accommodation be provided in view of their security status and threat to their lives.
The Centre, through its counsel Anurag Ahluwalia, appearing for Ministry of Home Affairs (MHA), submitted that there is no substantial reduction in the security given to Payal since she started living in the present bungalow.
"Delhi Police will take care of the security personnel who will be deployed at the residence where she will move," the MHA counsel said.
The Centre told the court that government accommodation, on security grounds, is given only to SPG protectees.
The high court had on July 12 given protection to them
against eviction.
The Jammu and Kashmir government opposed Payal's stay in the bungalow, saying it was faced with an extremely piquant situation as it does not have an appropriate accommodation to house the Chief Minister in Delhi befitting her position and security imperatives.
Meanwhile, Payal has filed an application seeking perjury proceedings against a Central government official for filing a false affidavit before the court that she and her children are not central government protectees.
They contended that the website of the Department of Hospitality and Protocol of Government of Jammu and Kashmir shows that the residence of Chief Minister of the state was 5, Prithviraj Road.
Their petition filed through advocate Amit Khemka, claimed that they moved high court as Omar Abdullah in his response to the estate officer's show cause notice had said he was no longer in occupation of the premises and, hence the authority was free to take over the premises.
The petitioners have contended that the eviction order was passed without allowing them to lead evidence and without granting any personal hearing to them.
As per the eviction order, the petitioners were given 15 days to vacate the premises.
Payal, in her plea, said she has a flat in the city, but it would be "totally insufficient for making elaborate security arrangements for their protection" as there were other flats in the same building.