Waratah-Wynyard councillor Darren Fairbrother said he won't resign because the Local Government Act currently allows those sentenced for a summary offence to continue representing their community.

Despite ruling out changes before this year's local government elections, Premier Jeremy Rockliff has asked Local Government Minister Nic Street to consider all options when it comes to addressing the issue.

"Changing the eligibility for elected representatives at any level of government is a serious issue that would need to be progressed transparently and with broad consultation," a government spokesperson said.

"The Premier has, however, asked the Minister for Local Government to consider options for addressing this issue over the medium term.

"The Minister for Local Government has asked the director (of local government) to look at all avenues available to either the director or the minister under the act such as a performance improvement direction, to reinforce the unacceptable nature of this behaviour."

With the issue attracting "significant interest", Waratah-Wynyard general manager Shane Crawford said it's important to clarify the misconception that the council can "sack" a councillor or remove them from their position.