The police have been heavily criticised, with many on social media alleging that officers attacked students with sticks and tear gas when they were peacefully protesting.
But Mr Randhawa said students and locals threw stones at the police first, adding that 30 policemen were injured.
“We will identify outside protesters and take action against them,” he said.
Live footage from the northern city of Lucknow on Monday showed students at Nadwa university throwing stones at security forces, who retaliated by throwing the stones back at them.
The students have been locked inside the campus.
Local television footage also showed officers hitting students with large sticks.
The situation remains tense and more protests are expected. Students at the prestigious Indian Institute of Technology in the southern city of Chennai (formerly Madras) have already announced a protest this afternoon.
And students in Delhi University have announced that they are boycotting examinations in solidarity.
On Sunday, hundreds of students across Indian cities came out in support of those protesting in Jamia Millia Islamia.
In the northern city of Aligarh, students of Aligarh Muslim University clashed with police, prompting the university to close down the campus until 5 January.
A large protest also broke out in the southern city of Hyderabad, as students of Maulana Azad Urdu University carried slogans against the police action in Delhi.
In India’s financial capital, Mumbai, students of the Tata Institute of Social Sciences held a candlelit march.
Some students in Delhi also alleged that police sexually harassed and assaulted students on Sunday.
Students in other cities like Varanasi and Kolkata also held marches in solidarity throughout Sunday.
Why is the law so divisive?
The law allows non-Muslims from Bangladesh, Pakistan and Afghanistan, who entered India illegally, to become citizens.
The Hindu-nationalist BJP government argues that the law aims to accommodate those who have fled religious persecution.
Critics say the law is part of the government’s agenda to marginalise Muslims, and that it violates secular principles enshrined in the constitution.
Earlier this week the United Nations Human Rights office voiced concern that the new law was fundamentally discriminatory in nature.
The government denies any religious bias and says Muslims are not covered by the new law because they are not religious minorities, and therefore do not need India’s protection.
Meanwhile, people in Assam fear that they will be “overrun” by illegal non-Muslim migrants from neighbouring Bangladesh.
They argue that outsiders will take over their land and jobs – eventually dominating their culture and identity.
The protests in Assam have little to do with concerns about the exclusionary nature of the law and the threat to secularism.
They have more to do with indigenous fears about being demographically and culturally swamped by “outsiders”.
