Expressing surprise over the petition, a bench headed by Chief Justie S A Bobde said this was the first time that someone was seeking that an Act be declared as constitutional.
The bench, also comprising justices B R Gavai and Surya Kant, said it will hear the petitions challenging validity of CAA when the violence stops.
"There is so much of violence going on. The country is going through difficult times and the endeavour should be for peace... This court's job is to determine validity of a law and not declare it as constitutional," the CJI Bobde said during the hearing.
The observation was made after advocate Vineet Dhanda sought the court's intervention to declare CAA as constitutional and a direction to all states for implementation of the Act.
It is only the Supreme Court which can help in clarification of the present situation and guide "confused" citizens of this country who are being misguided, he said.
As the bench remained unimpressed, the counsel appearing for petitioner Puneet Kaur Dhanda, withdrew the petition with liberty to intervene in the similar matters.
The apex court in its order said, "After some arguments, counsel appearing for the petitioner prays for withdrawal of this petition with liberty to intervene in the petition(s) on the similar issue pending before this Court. Prayer is allowed. Accordingly, the writ petition is dismissed as withdrawn with the liberty aforesaid."
The plea had also sought action against activists and media houses for "spreading rumours".
"After the enactment for the bill was introduced the political persons belonging to various political parties across India started misguiding and spreading false rumours and hereby creating a sense of terror and concern in the minds of community belonging to Muslim people across the country.
"The political persons belonging to various political parties which are out of power hatched a conspiracy against the government which has passed an Act named Citizenship Amendment Act, 2019 concerning the minorities in countries like Afghanistan, Bangladesh, Pakistan," the plea said.
It said politicians with a vendetta against the government and its "progressive approach" have created an environment of "hatred, fear, violence" in various parts of the country for their vested political interest as a result of which around 50 lives have been lost in various parts of the country and public property worth hundreds of crores has been destroyed.
"The negative environment of fear and violence has resulted not only in the loss of precious lives, damage to public property but also has caused huge economic loss across the country and has also bought a bad name to our country," it said.
The plea sought directions to extensively publicise through newspapers, electronic media and other means on the issue of Citizenship Amendment Act, 2019 and clarify that it is not against the Constitution of India.
On December 18, the apex court had agreed to examine the constitutional validity of the CAA, but refused to stay its operation.
The newly amended law seeks to grant citizenship to non-Muslim 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.
The apex court had earlier had fixed a batch of 59 petitions, including those filed by the Indian Union Muslim League (IUML) and Congress leader Jairam Ramesh, for hearing on January 22.
Several petitions have been filed challenging the constitutional validity of the Act including by RJD leader Manoj Jha, Trinamool Congress MP Mahua Moitra and AIMIM leader Asaduddin Owaisi.
Other petitioners including 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.