Here are the latest developments:
In Delhi, over 100 protesters were detained while marching near Shastri Bhawan in the heart of the capital, and were moved away in buses. They covered a distance of 2 km by foot from Mandi House to Shastri Bhawan. There were students from Jawaharlal Nehru University (JNU), Delhi University and Jamia in it. They were seeking Ms Irani's, Hyderabad University Vice Chancellor Appa Rao and Mr Dattatreya's resignation.
In Chennai, about 60 protesters were detained who were also protesting against the death of three medical students who allegedly committed suicide in Tamil Nadu's Villupuram.
The bodies of the three young women were pulled out of a well just opposite their medical college. A suicide note that they allegedly wrote described the appalling lack of even basic facilities at the college and their struggle to be heard by the administration.
Student organisations from across the country have called for a strike in all universities to protest against the death of Rohith Vemula, 26, who committed suicide at the Hyderabad Central University 10 days ago.
200 student associations have set up a national joint action committee, which plans to mark Rohith's birthday on Saturday, January 30, with a Chalo Delhi (Let's march to Delhi) protest. Rohith would have turned 27.
At Hyderabad Central University, students have been on a relay hunger strike in protest against Rohith's death and the punishment that led to it. One of seven fasting students was shifted to the university's health centre on Tuesday, and is now said to be in stable condition. Three students from JNU are also on indefinite hunger strike in solidarity with Hyderabad university student protestors.
The university's interim Vice Chancellor Vipin Srivastava has made multiple appeals in the two days since his appointment, to students to call off their protests.
Mr Srivastava took interim charge after the university's Vice Chancellor Professor Appa Rao Podile went on indefinite leave on Sunday. Student protesters accuse Prof Podile of punishing Rohith and the other Dalit students under political pressure.
Rohith and the others were suspended over a clash with activists of the ABVP, the BJP's student wing. Protesters have alleged that the Dalit research scholars were subjected to caste discrimination. They have rejected a move by the university to revoke the suspension of the four students punished along with Rohith and have demanded the sacking of the university vice chancellor and union ministers.
They allege that pressure from Mr Dattatreya, labour minister and BJP lawmaker from Secunderabad, resulted in Ms Irani's education ministry sending repeated reminders to the university, forcing it to punish the students.