The SNP-Green government at Holyrood has committed to holding a citizens’ assembly on how to replace council tax.
With parties now campaigning for May’s local elections, Mr Harvie told the BBC that “deeper reform” was needed.
However the government has previously said council tax reforms are unlikely to take effect during the current term.
Public finance minister Tom Arthur told MSPs in March that legislation would be needed to set up a new tax system, and that change would “go beyond the lifetime of this parliament”.
Mr Harvie is now a government minister, thanks to the partnership agreement sealed by the SNP and Greens following the 2021 Holyrood election.
Part of that agreement was to hold a citizens’ assembly on reform of the council tax – something both parties have pledged to pursue for years.
Councils were also given the freedom to set local rates this year, for the first time under the SNP, after years of council tax freezes.
Mr Harvie told the BBC’s Good Morning Scotland programme that a fundamental review of council financing was needed, “rather than this annual haggling over how much the budget would be from central government”.
He said: “In a lot of other European countries it would be bizarre that local councils would be so dependent on a single block grant. They have more of their own powers.
“We have already made a start – we have achieved significant change to make small steps towards local empowerment, local financial powers for councils, but we need to do much more.
“We have a commitment in the Scottish Parliament to have a citizens assembly on reforming council tax. That has been deadlocked parliament after parliament.
“Since 1999, the Scottish Parliament has failed to resolve this problem of a broken council tax system. We need to do that, and we believe that a citizens’ assembly can cut through the party political deadlock in a way that so far the Scottish Parliament has not managed.”
Four out of five parties at Holyrood support scrapping and replacing the council tax – including the SNP, which has pledged to scrap the tax at each election since 2007.
In its local elections manifesto Scottish Labour pledged to “abolish the unfair council tax and replace it with a fairer alternative based on property values and the ability to pay”, while the Lib Dems also support its “long-overdue replacement”.
Even the Scottish Conservatives are not entirely opposed to reform, calling the system “outdated” but a stable form of revenue for local services.
The Scottish government has promised to embark on a series of consultations, culminating in a citizens’ assembly which will examine how local government should be funded.
However Tom Arthur told Holyrood’s finance committee in March that he could not give a “concrete timescale” for changes.
He said: “Going from where we are now to a fully embedded and operational new system would go beyond the lifetime of this session of parliament.
“However, the commitment in this session is to do the groundwork at pace to establish the citizens assembly and allow it to be able to report back to parliament in sufficient time so that parliament can consider its response.”