Two councils are involved in this – Argyll and Bute had announced a 10% rise while Inverclyde backed an 8.2% increase.
They will now ask councillors to vote for a freeze in return for additional funds from the Scottish government.
Government Finance Secretary Shona Robison said, if approved, it meant households across the whole country would benefit from help during the cost of living crisis.
First Minister Humza Yousaf made the surprise announcement of a 12-month council tax freeze at the SNP conference last October.
The Scottish government said it would give local authorities £147m in compensation, as well as a share of £62.7m if they implemented the policy.
Most councils voted for a freeze but Argyll and Inverclyde said increases were the only way to maintain jobs and services.
Cardross, Helensburgh, Rhu, Garelochhead, Arrtochar and the Rosneath Peninsula are all in Argyll, which was the first council to break ranks, said the increase would help overcome a £40m funding gap.
But the authority said it had now been offered extra money for severe weather costs, and freezing the tax rates would help unlock £6.26m in extra funds.
Argyll and Bute Council leader Robin Currie said he was persuaded to reconsider following discussions with the Scottish government in recent weeks.
He said an extra £2.3m had been offered to support the impact of severe weather last autumn, and a council tax freeze would release other government funding, meaning the authority stood to gain an extra £6.26m in total.
Mr Currie said: “We made a very strong case for that to the Scottish government at a meeting we asked for in January this year.
“We have continued to press ministers ever since on a range of other issues. We are of course delighted that they have listened to our calls for severe weather support, and that they have now provided for Argyll and Bute that extra assistance that we are fighting for.”
Mr Currie said he would now be recommending a council tax freeze at a special meeting of the council next month.
Ms Robison said the council freeze would benefit people in every part of Scotland during the ongoing cost of living crisis.
“If the councils proceed with these decisions, council tax will effectively be frozen across the whole of Scotland, with households in 31 of Scotland’s 32 local authorities having a simple freeze in their council tax next year, and those in Inverclyde receiving a one-off rebate to reverse the impact of their 8.2% increase,” she added.
West Clyde Street on the seafront in Helensburgh. Picture by Bill Heaney