Victorian Education Minister Gabrielle Williams put the sweetened offer to the Australian Education Union's state branch on Monday morning.
If it is rejected, thousands of teachers and support staff educators are expected to stop work for 24 hours on August 19, the third strike since March.
The new offer adds to the state Labor government's previous proposal of a 28.3 per cent pay rise over four years - narrowly rejected by the union's members in July.
Under the new offer, staff will also receive a $2000 bonus payment once the agreement begins, with a one per cent annual lump-sum payment for those at the top of their pay scale.
Existing caps for face-to-face teaching hours would also be embedded in the deal, while a previous offer to reduce annual meeting times would be preserved.
The union's joint primary and secondary sector council was scheduled to meet at 5pm on Monday to decide whether to put the offer to its members for a vote.
"The council will give serious consideration to what's been put on the table this morning," the union's Victorian Branch president Justin Mullaly told reporters on Monday.
Mr Mullaly described the offer as "significant" and said it needed to be considered within the context of the broader negotiations.
"The offer builds on the (July 17) proposal by the government, as well as building on the one that was delivered in May this year," he said.
He would not be drawn on if or when the offer would go to a vote, but said the looming strikes would be factored in when considering next steps.
Negotiations between the state Labor government and union have dragged on for more than a year, boiling over into two statewide strikes.
An estimated 20,000 protesters marched through Melbourne's city centre in July after 51 per cent of unionised educators voted to reject the state government's latest offer.
An earlier strike in March attracted an estimated crowd of 35,000 people in central Melbourne.
Monday's offer is the first to be put to the union since Ms Williams took over as education minister on Tuesday, replacing now-premier Ben Carroll.
"We of course hope that our teachers and education support staff will have a close look at this offer and understand that we come to this in good faith," she said.
She labelled the offer "incredibly attractive" and said it fell within the range of previous cost estimates, at about $5 billion over the length of the agreement.
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