Next week's strike action in Shetland has also been called off after local union representatives decided to call time on the national talks. Aberdeen and Fife are said to be close to a settlement.
Any larger breakthrough in the national pay dispute will depend on the outcome of the meeting today (Friday) of the employers and Unison at the Scottish Joint Council. A major rally is still planned tomorrow (Saturday) in Glasgow in support of the nursery nurses' campaign.
Unison leaders have already rejected the outline national framework for local settlements as "flawed" and declined to comment on why branches had concluded deals.
Joe di Paolo, the union's Scottish organiser, said: "We asked for pound;18,000 to pound;21,000. They're offering pound;15,000 to pound;18,000.
Their top line is our bottom line. We have already seen these figures and they are not acceptable."
In contrast, Mr Watters hailed the South Lanarkshire deal, pointing out that it was always the intention of negotiators to reach agreements at local level within a national framework.
He said that the deal would mean a pound;2,000 rise for fully qualified nursery nurses working a full year for 37 hours a week. "That represents a 12.5 per cent increase on top of the 4 per cent increase in April this year. Term-time nursery nurses will get a 6.5 per cent increase on top of the 4 per cent," Mr Watters said.
The deal is being backdated to October.
Mr Watters this week wrote to MSPs and MPs to explain the Cosla offer, which is close to the South Lanarkshire agreement. "The proposed grades offer pound;18,000 per year to a fully qualified, competent nursery nurse - a rise of between 6.7 per cent and 12.5 per cent," he says.
"We believe that our proposal, which would give a nursery nurse pound;9.33 per hour, is fair and reasonable and that local negotiators can bring about satisfactory settlements based on our guidance," Mr Watters writes.
In Shetland, Brian Smith, Unison's branch chairman, said that while talks on backdating the offer would continue, nursery nurses there had agreed not to join next week's strike.
"This is a breakthrough. There is no prospect at present of any agreement between the union and Cosla at national level. Pending further discussions concerning detailed aspects of the offer, members are very happy with progress so far. What has been offered is a substantial improvement," Mr Smith said.