By Justin Parkinson
BBC News education reporter at the AUT council
Lecturers boycotting exam-marking over a pay dispute should accept the "very generous" deal on offer, the new education secretary said.
Lecturers say students are being graded on part of their degrees
Alan Johnson said it would be "incredible" if union leaders did not put the 12.6% offer to their members.
Lecturers at their annual council in Scarborough voted to continue the boycott which threatens to disrupt thousands of graduations this summer.
The Association of University Teachers warned universities face "meltdown".
The union has turned down a 12.6% pay rise over three years.
The education secretary urged them to accept the deal.
"The employers have made a very decent offer, actually a very generous offer, but I hope the unions now put it to their members.
"I think if they do it will be accepted."
But the AUT and its fellow higher education union Natfhe are calling for a rise nearer 25% over the next few years.
Both are refusing to mark exams or coursework. The AUT is also boycotting exam-setting.
AUT general secretary Sally Hunt says universities face "meltdown" unless the dispute is resolved.
Delegates in Scarborough said universities were threatening to withdraw pay in an effort to force lecturers to resume marking.
Staff had been sent "intimidatory" emails to this effect, the council heard.
Increasing numbers of student unions have complained that any disruption to graduations will damage employment prospects.
But John Fitzpatrick, of Kent University, said: "We are a bit too timid sometimes about this. We shouldn't allow it to be exaggerated."
He added: "We are not doctors or nurses."
Joanna Bryson, from Bath University, added: "Our students' education is the most important thing and that education is more important than their degrees, and that is why I can do this."
Jillian Howie, from Liverpool, said universities were resorting to measures such as "marking by average" or using the previous year's results to overcome the boycott.
The lecturers say that students are being judged on just part of their degree course.
In future, Ms Howie said, "we will ask doctors what year they graduated and they will say 'it was the year we didn't do ears as part of our third year paper'".
The Universities and Colleges Employers' Association (UCEA) increased its pay offer from 3% for this year and next year to 12.6% over three years. It says the offer is "final".
But unions refused this at a meeting on Monday as being too little to compensate for 20 years of "decreasing earnings" in real terms.
Since then, Aberdeen University has broken away from the UCEA proposals, telling all lecturers they will get 12.5% over three years.
The university is asking union members who do not wish to accept this to write a letter to that effect.
Alexander Arthur, a lecturer at the university, said this reflected a "profound anxiety" among employers.