Elizabeth Maginnis, the local authorities' chief negotiator, said she had no objection to a meeting on "points of clarification" but insisted the current offer was final.
The chink of light in what otherwise appears to be stalemate follows last week's rejection by the Educational Institute of Scotland, the lead union negotiator, and other unions of the complex pay and conditions package.
The EIS wants further talks but the Scottish Secondary Teachers' Association is to recommend that members reject the offer in a ballot. The National Association of Schoolmasters Union of Women Teachers also dismisses it.
The employers have rejigged the figures to give teachers an average rise of around 18 per cent over three years, adding pound;200 million to the annual pay bill, in return for changes in conditions of service.
Both sides maintain they have moved substantially towards each other's position, yet no agreement is in sight after 18 months of talks about principles in the Millennium Review and 17 hours of detailed negotiations. Last week's critical meeting lasted until the small hours of Friday morning.
Mrs Maginnis said: "Management has made its final offer and has moved very significantly towards meeting the majority of teachers' concerns as laid out in their counter-offer and that is acknowledged by the EIS.
"There comes a point where negotiations have to stop and unions have to put the offer to their members. It is a fair offer and reflects our concerns for delivering a modern, flexible education service in the year 2000 and beyond and I regret the EIS is not putting the offer before members.
"If they do want further points of clarification I have no objection to that but that's the final offer."
Ronnie Smith, the EIS's general secretary, said the latest offer was "markedly closer" to the union's counter-proposals. It would mean real benefits for some teachers, cuts in class contact time for primary staff and the removal of the requirement that teachers work an extra 70 hours. But Mr Smith spelt out several key areas for further negotiation (see below).