The Supreme Court would not grant a stay before hearing from the government, which has argued the law is a humanitarian gesture allowing citizenship for people fleeing religious persecution in Muslim-majority Pakistan, Bangladesh and Afghanistan.
Chief Justice Sharad Arvind Bobde, the head of a three-judge panel, told the courtroom he will decide on the case only after the government has replied to all the petitions in four weeks. He also asked a larger, five-judge constitutional panel to take part in the decision.
The law Parliament approved in December sparked vehement opposition. Protesters, political opponents and constitutional lawyers have said it is discriminatory because it excludes Muslims.
The nationwide protests numbering in the tens of thousands appear to be the fiercest public criticism Prime Minister Narendra Modi's Hindu nationalist-led government has faced.
Modi's party has downplayed the protests as orchestrated by opponents. His powerful Home Minister Amit Shah said the government will not retreat on the law.
"Those who want to protest may continue doing so," Shah said Tuesday at a public rally in Lucknow.
Most of the petitions argue that by excluding Muslims, the law undermines the first sentence of the preamble to the Indian Constitution, which defines the country as secular, and violates Article 14, which guarantees equality before the law.
"We believe the court will certainly take into consideration the views expressed by all these sections of people, and they will come to a conclusion that it (law) is against the Constitution of India," said petitioner K. M. Kader Mohideen.
Modi's government and proponents of the changes say Muslim immigrants still could attain citizenship through the existing naturalization process.
"Because it is a well-drafted legislation, with a specific purpose, for a specific group of people, there is really no problem on it passing the muster," said Aishwarya Bhati, a senior advocate at the Supreme Court who supports the government's move.
Those who oppose the law believe the government will argue it is not based on an immigrant's religion, but on religious persecution in the three countries.
"If you discriminate on the grounds of religion, that itself is prohibited in the constitution," said Colin Gonsalves, a senior advocate at the Supreme Court and founder of the Human Rights Law Network, which filed two of the petitions.
Gonsalves, however, said it is unlikely judges will strike down or alter the law, echoing the fears of many Indians who oppose the measure and are questioning the court's independence.
"The Supreme Court is no longer the beacon light of democracy in India," Gonsalves said. "Judges today are political, liaised, in a wrong way, that is, towards government."
Jay Panda, the national vice president and spokesman of Modi's party, said that most of the protests against the law involved poor, illiterate people, many of whom had not read the amendment and are being misled.
"Some people are deliberately provoking them," said Panda, referring to the monthlong sit-in by hundreds of Muslim women, many of them homemakers, on the outskirts of India's capital.
Critics also say that the new citizenship law discriminates because it lowers the minimum residence requirement to five years for Hindu, Sikh, Buddhist, Jain, Parsi and Christian migrants, while keeping it at 11 years for Muslims and other religious groups.
India has a vast, undocumented immigrant population among its 1.3 billion people, with many of them living in the country for generations.
In the northeastern state of Assam, the center of sometimes-violent opposition to immigrants from neighboring Bangladesh, the government last year said 1.9 million people had failed to prove their Indian citizenship.
Those people must make their case for citizenship in front of quasi-legal tribunals, and could be detained or deported if the tribunals deem them foreigners.