He said it wanted time to respond to pleas which have not been served on it.
Senior advocate Kapil Sibal urged the bench to put on hold operation of CAA and postpone exercise of the National
Population Register (NPR) for the time being.
The court said it will not grant any stay on CAA without hearing the Centre on the matter.
"Will pass order on granting any interim relief to petitioner opposing CAA after four weeks," the bench said.
The CAA seeks to grant citizenship to migrants belonging to Hindu, Sikh, Buddhist, Christian, Jain and Parsi communities who came to the country from Pakistan, Bangladesh and Afghanistan on or before December 31, 2014.
President Ram Nath Kovind gave assent to the Citizenship (Amendment) Bill, 2019 on December 12, turning it into an Act.
Several petitions have been filed challenging the constitutional validity of the CAA, including by RJD leader Manoj Jha, Trinamool Congress MP Mahua Moitra, AIMIM leader Asaduddin Owaisi.
Several other petitioners include Muslim body Jamiat Ulama-i-Hind, All Assam Students Union (AASU), Peace Party, CPI, NGOs 'Rihai Manch' and Citizens Against Hate, advocate M L Sharma, and law students have also approached the apex court challenging the Act.