Metropolitan Magistrate Gomati Manocha deferred the matter after counsel appearing for them sought adjournment due to the ongoing lawyers strike.
The court also allowed the separate pleas of Gadkari and Singh seeking exemption from personal appearance for the day.
The magistrate directed the advocates representing both the leaders to argue the matter on the next date of hearing.
Earlier, Singh had contended before the court that Gadkari has not placed any "admissible evidence" against him in the defamation complaint.
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Gadkari, Union Minister of Road Transport and Highways, had earlier ruled out any possibility of reaching a compromise with Singh, saying he would not withdraw his plea unless the Congress leader takes back his statement of 2012 on his alleged business links with the then MP Ajay Sancheti.
Singh, who was summoned as an accused in the complaint, had said "in my life I have never withdrawn my statement".
The criminal defamation complaint was filed by Gadkari in 2012 against Singh who had alleged that the former BJP chief had business links with Sancheti.
In the complaint, Gadkari had alleged that Singh had accused him of pocketing Rs 490 crore in coal block allocation to Sancheti.
Gadkari, in his statement recorded in the court earlier, had denied having any business ties with Sancheti and said that Singh levelled "totally false and defamatory" allegations against him to "give the impression that I have been responsible for allocation of the coal mines" to Sancheti.