The protesters wear Muslim caps and many of the women wear the hijab headscarves, but they also sing national songs, read out sections of the constitution and carry pictures of independence hero Mahatma Gandhi and B.R. Ambedkar, who led the drafting of the constitution.
"This tricolor is our symbol against fascism," Asaduddin Owaisi, an MP who heads a Muslim party, said of India's saffron, white and green flag during a rally in the southern city of Hyderabad at the weekend.
He also asked the crowd to recite the preamble of the constitution in both English and in the Urdu language spoken by many Muslims, and urged them to fly the Indian flag at their homes.
In a column on Saturday, prominent editor and political commentator Shekhar Gupta said the protests had led to what he called the "rise of a new Indian Muslim... Not afraid to look Muslim, and not shy of flaunting her nationalism."
At least 21 people have died in the protests against the new citizenship law and a planned national register of citizens, which protesters say contravene the secular constitution and discriminate against Muslims.
The law gives non-Muslim minorities from Afghanistan, Bangladesh and Pakistan who fled to India before 2015 a pathway to citizenship. It does not apply to Muslims.
India's Muslims, who form about 14% of the Hindu-majority country's 1.3 billion people, say they are often called anti-national and Pakistani. Muslim Pakistan was carved out of British colonial India when the countries gained independence in their bloody 1947 partition and have since fought three wars.
Protesters say displays of patriotism help dispel the notion that protests are a Muslim issue. Tens of thousands of Hindus have also joined.
"Making this a Muslim protest just gives another stick to the government to delegitimise the movement," said law student and protest organizer Hamza Tariq, 22, in the city of Bengaluru.
The demonstrations across India are the biggest challenge to Modi since he first came to power in 2014.
Modi himself appeared to make a veiled allusion to Muslims resorting to violence during the protests.
"You can tell who these arsonists are by their clothes," he said in an address last week, in comments condemned by Muslim leaders.
Muslim protesters at the Jamia Millia Islamia University in New Delhi said that police who stormed the campus on Dec. 15 with tear gas and batons called them "Pakistani citizens" and "Islamic militants."
Prabhat Kumar, a Hindu student at Jamia, said: "This law is differentiating between communities which is against the constitution."When will Muslims speak if not now? This is the right time to speak and we will stand with them till the end."