Universities have promised an "improved and realistic" pay deal in an effort to end a lecturers' marking boycott.
Aberdeen was the second university to make a local offer
The move comes after St Andrews and Aberdeen universities both offered academics a higher salary rise than that agreed nationally by employers.
The Association of Union Teachers rejected the individual proposals but said they could be a "starting point" towards a UK-wide agreement.
The dispute threatens to disrupt graduations across the UK.
Aberdeen and St Andrews are offering a 5% pay rise from August. This would be followed by 3.5% in each of the next two years.
The Universities and Colleges Employers' Association's (UCEA) offer stands at 3% this year and 3% next. It has not yet suggested a new figure.
Two lecturers' unions, the AUT and Natfhe, are boycotting all exam-marking and coursework assessment - and in the AUT's case exam-setting - until they see a "substantial" pay rise for members.
With graduations threatened, universities such as Cambridge and Keele have already set in motion "emergency measures" - such as using exam papers from other sources - the AUT said.
General secretary Sally Hunt said negotiations with employers had reached "crunch time".
The St Andrews and Aberdeen offers showed there was "more funding available", she added.
Ms Hunt said: "I suspect there was a panic in those universities about the impact the boycott was going to have. They are determined to resolve things."
A growing number of student unions are complaining that the boycott is damaging final-year undergraduates.
The AUT and Natfhe are to resume discussions with UCEA next Monday, under the auspices of the arbitration service Acas.
UCEA said it would be "putting an improved and realistic pay offer to them in the expectation that they will then immediately call off their industrial action".
Aberdeen University's senior vice-principal, Stephen Logan, said: "I feel I need to continue to do everything in my power to bring this dispute to an end."
He said he first offered a local settlement to representatives of the AUT - which represents academics in the older universities - more than eight weeks ago.
"As a result of these discussions I agreed to respect the AUT's preference for a national settlement until such a time that the industrial action became harmful for students," he said.
The AUT said its "appraisal olive branch" was on the basis that employers were "serious about their intention to deliver a credible offer to the unions".
Ms Hunt said: "We are pleased that both sides have managed to agree to talks on Monday as we want this dispute resolved as quickly as possible."
She added: "A failure to do so will be a huge insult to their staff, students and vice-chancellors who, like us, want this dispute sorted out."
Wait and see
Academics in Scotland's newer universities tend to be represented by the University Lecturers' Association in the Educational Institute of Scotland.
It is not in dispute, preferring to wait for the completion of national negotiations - though it has complained that some of its members have been coming under pressure to set exams normally set by AUT members.
National officer Marion Healy told BBC News her union hoped to be in a position following Monday's meeting with the employers to ballot its members on their offer, provided there was a "substantive improvement".
"We want to work constructively not only to maximise the pay of all our members but so that every institution ... can actually afford to make the payment, and there's no opt-out."