Green MSPs are to hold a vote in Holyrood in a bid to get the Scottish Government to scrap the "outdated unfair" council tax system.
The SNP had promised to abolish the charge when it was first elected to power in 2007, with ministers forced to go back on this two years later as there was "no consensus" in Holyrood for the change.
Since then the Scottish Government has made some reforms to the charge, which contributes towards council funds.
With the SNP now forming a minority administration, Greens believe they can build on the work of the Commission for Local Tax Reform, which recommended axing the tax in 2015.
Finance Secretary Derek Mackay insisted the Scottish Government was "committed to making local taxation more progressive", adding he was "open to further dialogue on options for local tax reform".
The Greens have already told SNP ministers they want changes to be made to the council tax system if they are to support the Government's budget next year.
Andy Wightman, the party's local government spokesman, said at the moment "the public are being penalised with an outdated, unfair system under which most households are paying the wrong amount".
Speaking ahead of a debate in the Scottish Parliament on Wednesday he added: "Successive Scottish Governments have ducked this issue but with a parliament of minorities, we have a chance to build on the agreement struck during the 2015 cross-party Commission on Local Tax Reform that the present council tax system must end."
Pressure from the Greens resulted in the SNP making changes to income tax in Scotland, Mr Wightman argued, saying this had "resulted in a shift toward a fairer system of income tax, with lower earners paying less and higher earners paying more".
He demanded: "We must see a shift in local tax so we have a fairer system that gives local authorities flexibility to raise the funds they need for local services.
"I hope other parties agree that after years of talking, it's deeds not words that count, and we must see movement on this issue before the summer."
But Scottish Conservative local government spokesman Alexander Stewart said: "When the Greens call for a 'fairer' tax system, we all know what that means. They want to punish hard workers across the country.
"Even those on modest salaries, or living in very normal homes in certain parts of the country, would be hammered if this went through.
"Taxpayers in Scotland will be hoping the Greens' cosy relationship with the SNP, which has already seen two budgets go through, won't lead to these madcap changes too."
Mr Mackay said: "This Government remains committed to making local taxation more progressive and we have made clear that we are open to further dialogue on options for local tax reform."
The Finance Secretary said ministers, together with the local government body Cosla, had launched a Local Governance Review, "which will make sure communities have more say about how public services in their area are run".
Mr Mackay continued: "A transformation of local democracy can be best achieved by looking at how public services work with each other and inviting communities to identify the powers and resources they need to thrive.
"We have also made council tax fairer and included a 25% increase to the child allowance in the reforms that were introduced last year.
"The scheme was extended in April 2017 to provide relief for low to middle income households from the impact of the council tax reforms on properties in bands E-H.
"And we have invested over £1.4 billion in the council tax reduction scheme since 2013/14, assisting almost half a million households each year to meet their council tax.
"In addition, the Scottish Land Commission is researching land value tax in the wider context of land reform."
But Scottish Labour finance spokesman James Kelly, said: "The SNP came to power more than ten years ago promising to scrap the unfair council tax yet its successive governments have failed to do so.
"Scottish Labour has put forward proposals which would see the council tax abolished and a new property tax introduced which would make 80% of households better off. "