Scots want rich households to pay more council tax as part of a wholesale reform of the local rates system.
A major consultation by the SNP Government found that eight out of 10 respondents are in favour of overhauling the current set-up, which is still largely based on property values from 1991.
The most popular option for change was a revalued 14-band system that would ask owners of higher-value homes to contribute more.
Successive Nationalist administrations have ducked the issue despite being first elected to Holyrood in 2007 on a manifesto that included a pledge to scrap the council tax.
SNP ministers have previously blamed a lack of "consensus" at Holyrood on the issue for the failure to reform the system.
But an analysis of the government's own consultation by Tax Justice Scotland - a campaign backed by more than 50 organisations including charities and trade unions - found overwhelming support for change and little appetite for retaining the status quo.
Katherine May, head of Oxfam Scotland, said: "Scotland has built a Parliament, lived through seven First Ministers, and watched a generation grow up since homes were last properly valued.
"For years we've been told council tax reform can't happen without consensus.
This consultation suggests Scotland has already made up its mind.
"Scots understand a simple principle - when property wealth has grown so dramatically over the last 35 years, those with the most valuable homes should contribute more.
"Council tax is one of the few ways Scotland taxes wealth, yet it's still based on property values from 1991.
It's long past time for this tax to reflect modern reality.
The challenge now isn't building support for reform.
It's finding the political courage to deliver it." John Swinney announced....
