The students are from East West, North South, South East and BRAC universities in the capital.
Metropolitan Magistrate Abdullah Al Masud rejected their bail pleas and granted police two days on Tuesday to grill the students.
Fourteen of them were arrested in a case started at Badda Police Station and the others in Bhatara Police Station.
Police alleged in a remand petition that the students are members of militant groups.
Defence lawyer AKM Muhiuddin Faruq alleged police tortured the ‘innocent’ students in custody.
Kabir Hossain, the lawyer for East West University student Ridwan Ahmed, alleged police beat up and broke a finger of his finger.
The lawyers for Masad Mortuza Bin Ahad, Foyez Ahmed Adnan and Azizul Hakim also alleged their clients were beat up at the police stations.
Police, however, claimed the students were slightly injured in scuffle during arrest.
The other remanded students are Rislatul Ferdous, Rashedul Islam, ‘Bayezid’, Mushfiqur Rahman, Iftekhar Ahmed, Reza Rifat Akhlaq, AHM Khalid Reza, Tariqul Islam, Noor Mohammad, Simanta Sarker, Iktider Hossain, Jahidul Haque, ‘Hasan’, Saber Ahmed, Mehedi Hasan, Shihab Shahriar, Shakhawat Hossain and Aminul Ehsan.
The students protesting for road safety measures and justice for traffic accidents clashed with police in the university areas on Monday.