Campaigners against hostile environment policies in higher education are calling on universities to suspend monitoring of international students’ attendance during strike action, because of growing fears their visas will be at risk if they choose not to cross picket lines.

Responding to a call-out to Guardian readers about ongoing industrial action in 60 universities across the UK, a number of international students said they were supportive of strike action but worried about failing to comply with attendance requirements with potential consequences for their visas.

“I would love to be able to act in solidarity with the strikes but because of my visa I have no choice but to cross picket lines and attend classes,” said one international student studying law at Edinburgh University. “This leads to quite a bit of guilt and anxiety, as I worry that I’m undermining the pickets by continuing to attend classes.”

Another, an international PhD student at Exeter University, said the issue was causing enormous stress. “As an international student, I’m required to somehow have my attendance documented. However, I can’t, as my supervisors were busy at the start and now are striking.

“I will have to explain this absence and answer questions about my time management, even though it’s outside of my control. Many international students are feeling pressured to cross the picket line, and cannot afford to fall behind/have absences.”

A university administrator at one Russell Group university said she had spent the morning dealing with significant numbers of panicked students, especially international students on Tier 4 visas whose attendance is routinely monitored. “Our student welfare services are stretched at the best of times, now, they are overrun,” she said.

Ordinarily, if an international student misses 10 consecutive teaching sessions, the university is obliged to report them to the immigration authorities. According to the University and College Union (UCU), which represents university workers, an absence due to industrial action should not be included, but if a Tier 4 sponsored student misses a lecture by non-striking staff to show support for the strike, this would be considered an unauthorised absence and would therefore count.

There are also fears that international students may be unclear as to whether their lecturer is on strike or not – not all staff are involved in industrial action – and erroneously skip a lecture thinking it has been cancelled.

More than 40,000 university staff – including academics, technicians, librarians and professional services staff – are in the middle of eight days of strike action over pay, pensions and working conditions, with picket lines disrupting campuses across the UK.

Around a million students are affected by the industrial action. Many have come out in support of their lecturers and other university staff on picket lines and there have been a number of student occupations of university buildings at Edinburgh, Strathclyde and Stirling universities. Of the students who contacted the Guardian, most said they supported the strikes, with only a small number demanding compensation.

Seventy student activist groups and student unions issued a statement in support of the UCU strikes, calling on university managers to issue a public statement cancelling all student attendance registers on strike days, including classes ongoing during strike action.

“Monitoring migrant students’ attendance on strike days amounts to the cynical use of students’ visa precarity against workers’ right to industrial action,” said the statement, which was supported by groups including the National Union of Students, People & Planet, Rent Strike and Student Climate Action.

Earlier this week, the University of Liverpool came in for criticism after managers sent an email to undergraduates on Friday warning them it was unlawful to join pickets. In the same email, international students were informed that anyone who chose not to cross picket lines to attend teaching sessions risked jeopardising their visa.

As a result nine external examiners in the school of law resigned their roles in protest, accusing Liverpool of misrepresenting the law regarding support for official pickets and of “weaponising” the UK immigration system against visa-holding students.

The immigration advisory service at Goldsmiths, University of London, emailed international students on 22 November, telling them their visa status would not be affected by academic sessions cancelled because of industrial action, but warning they must attend academic sessions which take place as scheduled.

Robert Liow, international students’ officer at Goldsmiths, said: “This creates a climate of fear. International students on Tier 4 visas have been stripped of their right to choose solidarity and not cross the picket line during the strikes with punitive action that puts their visa status and future career in the UK at risk.”

A spokesperson for Goldsmiths, University of London, said the email was a regular reminder sent in the autumn term every year, as part of a range of support and information shared with international students.

The UCU general secretary, Jo Grady, said: “Threatening students who simply want to support their striking lecturers is an underhand tactic that rather reeks of desperation. In the current climate universities should be doing all they can to show off the UK as a welcoming place for international students to come and study, not making short-term threats because they refuse to tackle serious problems at the heart of these disputes.”

The UCU is to re-ballot a further 13 universities ahead of possible further action in the new year. The re-ballots will start next week and will run until the end of January, to bolster support for a second wave of action if the disputes cannot be resolved.