The state government told a bench headed by Justice Madan B Lokur that it would be difficult to declare entire Agra as a heritage city.
The matter has been listed for further hearing on November 29.
The apex court had earlier given time till October 15 to the state, but it was extended today after Additional Solicitor General (ASG) Tushar Mehta and advocate Aishwarya Bhati, representing the Uttar Pradesh government, sought an extension.
He had said that the Archaeological Survey of India (ASI) was in the process of preparing a heritage plan for the Taj which would be filed with the UNESCO in three months.
The apex court had earlier asked the authorities to take a larger perspective on issues of pollution and green cover while preparing a vision document, saying that there will be no "second chance" to preserve the Taj Mahal.
The top court, while observing that the Taj Mahal would "of course be the centrepiece" of the matters to be considered, had said other issues like vehicular traffic, pollution from the industries operating in the Taj Trapezium Zone (TTZ) and the water level of river Yamuna, should also be looked into while preparing the vision document.
"If the Taj Mahal goes once, you will not get a second chance," a bench of Justices Madan B Lokur, S Abdul Nazeer and Deepak Gupta had told the project coordinator, who is involved in the process of preparing the vision document.
The state government had earlier said the School of Planning and Architecture in Delhi was preparing a vision document. Besides looking into the issue of protection of the Taj Mahal, they were also considering a larger comprehensive plan to deal with all these issues.
Environmentalist MC Mehta, the petitioner in the case relating to the protection of the Taj Mahal, had told the court that green cover in the area has reduced and there were encroachments in and outside the Yamuna floodplains there.
He referred to the apex court's 1996 order in the case and said several industries have come up in the area, with many of them operating beyond their capacity.