The court has also asked the Centre to consider floor test in the Uttarakhand Assembly.
The court had earlier decided May 3 as the next date of hearing.
An apex court bench headed by Justice Dipak Misra, had on April 27, directed to continue the President's Rule for the while.
The two-judge division bench, comprising of Justice Dipak Mishra and Justice Shiva Kirti Singh, had also asked several questions to the Centre asking it to justify imposition of President's rule in the state.
Court has asked the Attorney General to have a floor test under their supervision.
The apex court also sought to know whether disqualification of MLAs by the Uttarakhand Speaker is a relevant issue for the purpose of imposing President's rule under Article 356 and proceedings in the Uttarakhand assembly can be taken note of by the President for imposing his rule.
The President's Rule has imposed in the state on March 27.