BMC counsel Ashutosh Kumbhakoni sought additional time of two weeks.
Reservation of 20 per cent of beds was a condition which the Brihammumbai Municipal Corporation had put forth to give its land in Marol to the private company for construction of the hospital.
The High Court, in June, had appointed former Chief Justice of Allahabad High Court, F I Rebello, as mediator.
Kumbhakoni informed that the parties had had three meetings so far, and were likely to reach a settlement within two weeks.
Accordingly, the matter was adjourned.
The Seven Hills Group had earlier informed that it was ready to construct a separate 300-bed hospital within the hospital premises, where patients referred by civic hospitals will be treated.
The civic hospital authorities had alleged that poor patients were given scant attention by the Seven Hills management, and they were in fact discouraged from getting admitted.
Seven Hills, on the other hand, was aggrieved with the BMC for not issuing No-Objection Certificate (NOC) which it needed for a bank loan.