The Lucknow bench of the court, on the request of Additional Advocate General Bulbul Godiyal, adjourned the case till June 29.
On June 23, the court had directed the District Magistrate, Lucknow and Superintendent, Archaeological Survey of India (ASI) to open locks of the Imambaras of Lucknow.
A vacation division bench of Justices Arun Tandon and Anil Kumar has passed the order on a writ petition filed by one Masarrat Hussain.
The petitioner alleged that despite the court orders locks could not be opened.
Also Read
"On the request of additional advocate general the case was adjourned to June 29 as much as it is assured that the order of the Court shall be complied with," the court said.
The gates of the two monuments, controlled by ASI, have been locked by the supporters of Shia cleric Maulana Kalbe Jawwad. They are demanding sacking of Shia Waqf Board chairman Wasim Rizvi.
Jawwad and his supporters are protesting against Rizvi. They allege that he was corrupt and close to controversial UP minister Azam Khan.