Local government body Cosla has rejected the Scottish Government's funding offer for this year's budget, describing it as "totally unacceptable".
The organisation said the package put forward by Finance Secretary John Swinney in the 2016/17 draft budget is "an affront to local democracy".
The Scottish Local Government Partnership (SLGP), which represents Aberdeen City, Glasgow City, Renfrewshire and South Lanarkshire councils, said local authorities are being "held to ransom" and confirmed it is seeking legal advice over the deal.
Talks have been taking place between Mr Swinney and council leaders, with the deadline for accepting the deal put back for a second time to February 9.
The funding agreement from the Government includes extending the council tax freeze, £250 million for integrating health and social care services and maintaining the pupil/teacher ratio in schools.
Cosla says councils are facing £350 million of cuts, while some local authorities are considering breaking the council tax freeze.
Speaking after a meeting of council leaders in Edinburgh, Cosla president David O'Neill said: "Cosla has today rejected the package of measures for local government as totally unacceptable and an attack on our democratic mandate.
"Make no mistake, this is a hugely significant 3.5% cut for communities in Scotland, which will hit the most vulnerable in those communities because of decisions taken in Edinburgh.
"The £350 million cut is bad enough - but the way in which it will now be imposed on individual councils is even worse. The Scottish Government is basically forcing individual councils into having to accept the deal."
He added: "Sadly, I fully accept however that individual councils, due to the horrendous sanctions they would face, will find that they have no other option but to give in to central direction on this occasion.
"In imposing the deal on individual councils, the most vulnerable in our communities will be left to pick up the pieces."
Jenny Laing, leader of Aberdeen City Council and SLGP convener, said the relationship between the Scottish Government and councils is "broken".
Speaking after a meeting in Glasgow to discuss the settlement, she said: "This is the most significant grant cut ever applied to local government and when we've carried out our civic duty to question the settlement on behalf of our residents, we've been held to ransom by the Scottish Government's attempt to control decisions which should be made by democratically-elected representatives.
"The four SLGP councils provide services to more than 25% of citizens across Scotland. Refusing to give us appropriate levels of funding and trying to dictate to local government shows blatant disregard for those people.
"In addition, there are also questions around the legality of the minister's right to tie our hands in this way and we'll be seeking legal advice on that."
The SLGP also called for further devolution to local authorities, including employment support, fiscal powers, local energy and fuel poverty schemes and transport.
Opposition parties called on Mr Swinney to rethink the package.
Scottish Liberal Democrat leader Willie Rennie said: "The Government's relationship with local councils has reached an all-time low and it's time for him to stop his cuts to councils' budgets and lift the threat of massive fines if the council tax is raised.
"Instead of hammering councils' budgets John Swinney should be signing up to our progressive plan to raise £475 million a year for education by adding one pence on to each tax rate."
Scottish Labour communities spokesman Ken Macintosh said: "It looks like councils of all political make-ups have told the SNP Government that enough is enough. Resistance is growing to Swinney's attempts to bully communities into accepting his cuts.
"John Swinney must now rethink his plans to cut local services to the bone."
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