Union members had hoped Cosla would offer a new one year deal taking inflation into account.
She said discussions with Cosla on a range of local government finance matters were continuing.
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He argued that council body Cosla made a "mistake" in trying to "impose" pay restraint.
Ms Burgess told MSPs she favoured working with groups like council umbrella body Cosla.
It is now undoubtedly farewell to the concordat, occasionally billed as historic, between Ministers and Cosla.
The Convention of Scottish Local Authorities (Cosla) criticised the proposed move to self-financing through fees from 2004-05.
But David O'Neill, of council governing body Cosla, is unhappy at the reforms.
However, Cosla said increasing the original offer of 2.5% in the current economic climate would result in service and job cuts.
Pat Watters, former President of the Convention of Scottish Local Authorities (Cosla), will chair the the new Scottish Fire and Rescue Service.
The Convention of Scottish Local Authorities (Cosla) said it was pleased that the number of quangos would be reduced through the merger.
Councillor Michael Cook, vice-president of Cosla, said councils were already rising to the challenge and finding new ways of doing more with less.
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Cosla said the Scottish government had already made up its mind that a single police force and fire service was the way forward.
The call for action over the state of Scotland's roads was echoed by Cosla, the body which represents the majority of Scotland's local authorities.
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He said the government had reached an agreement with the COSLA leadership on an approach to delivering joint priorities between national and local government.
It was set up by the Scottish Executive after teachers and their local authority employers, the Convention of Scottish Local Authorities (Cosla), failed to agree on changes to pay and conditions.
Among the issues being discussed at the Love Cycling, Go Dutch conference, which is taking place at the Cosla Conference Centre in Haymarket, are better town planning and road-user awareness.
Environmental health and now local licensing standards officers will be responsible for enforcement - and COSLA and their professional bodies will be invited to join the implementation group to prepare local authorities for this responsibility.
Mr O'Neill said that Cosla could "not stand idly by and allow local government's reputation and the credibility of individual councils to take the hit for this because these welfare changes are not of our doing".
Cosla, the umbrella body for local authorities, said teachers in Scotland have one third of their week - three times as long as their counterparts in England and Wales - for preparing lessons, correction and marking.
Mr Smith went on to say it was "far from clear" that the government and Cosla were on the same page over the definition of maintaining staff numbers and the extent of the guarantee over compulsory redundancies.
Local government umbrella body Cosla said it was important the Scottish Police Authority robustly challenged and held the Chief Constable to account to ensure communities across Scotland continued to receive a high standard of policing and crime rates continued to fall.
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