More than 7,000 people have signed a petition calling for plans for the £395,000 sculpture at Flint Castle to be scrapped.
Flintshire council urged the Welsh Government to talk to the community before any "further action is taken".
The Welsh Government said it would listen to a range of views.
The design, said to represent the relationship between the Medieval monarchies of Europe and castles, was selected by a panel following a nation-wide competition.
The architects behind the design said it demonstrated "the unstable nature of the crown" but it has been criticised for symbolising the oppression of Welsh people.
The council said it was not privy to Cadw's proposals for the art installation before they were unveiled on Friday.
When opened in 2018, visitors will be able to walk along the sculpture, symbolic of a giant rusted crown. which could potentially stand 7m (23ft) high and 30m (98ft) wide.
The authority made clear it would not be funding the installation and Cadw would need planning consent before it could proceed.
It said the castle - one of the first built in Wales by Edward I - was under-funded compared to others in north Wales and Welsh Government cash was "vital" to allow it to fulfil its potential.
Derek Butler, cabinet member for economic development, said: "The council would welcome Welsh Government investment in any of the culture and heritage assets of the county following appropriate discussions with local communities and stakeholders and with the council itself."
A Welsh Government spokesman said: "We recognise that art divides opinions, encourages debate and can be interpreted in many ways and that combining history, art and place can often lead to powerful emotions and passions.
"These plans are about investing in Flint, increasing visitor numbers and growing the local economy."
Controversial plans for an iron ring sculpture accused of "insulting Wales" have prompted a council to distance itself from the project.