The Archaeological Survey of India (ASI) on Wednesday asked the Delhi High Court not to allow any activity or construction at the purported excavated mosque site near Jama Masjid.
The ASI also told the court that the protection of the site should be the responsibility of the Delhi Police.
The court last week put a stop on construction work at the site at Subhash Park and asked the ASI to investigate if the Akbarabadi Masjid, whose ruins were being claimed to have been found there, did exist or not.
During the hearing, police told the court that area legislator Shoaib Iqbal, who started construction on the site, should be directed not to create any tension.
Counsel appearing for police, Pawan Sharma, said, "We are complying with the high court order. Shoaib Iqbal be directed not to create any tension in the area."
A special bench of Acting Chief Justice AK Sikri, justice SK Kaul and justice Rajiv Shakdher reserved its order.
The Akhil Bharat Hindu Mahasabha (ABHM), a political outfit, filed an intervening application in the case and sought the removal of construction at the site, where a mosque was being built by some area residents.
Thousands of Muslims offered Friday prayers there claiming that the building remains found at the excavated site were ruins of a Mughal-era mosque.
The building's remains were discovered early this month during Delhi Metro work.
Some people from the area claimed that the ruins were those of the 17th century Mughal-era Akbarabadi mosque and started building a fresh structure at the site but the court put a stop to it.
Following the court order, the North Delhi Municipal Corporation and police cordoned off the area and handed over the site to the ASI.