Councillors from Kingborough Council in Tasmania's south have voted to support the removal of legislation which prevents same-sex couples from marrying.

The motion was passed five votes to three.

The council will now write to all Tasmanian senators and the federal member for Franklin, urging them to prioritise changing the Marriage Act to allow marriage equality.

Kingborough Mayor Steve Wass said the move was about removing discrimination.

"We value the differences in people and their perspective," he said.

"We'd like to build relationships based on mutual trust and we recognise the contributions of each and every individual in our municipality and we think maybe we need to keep this issue up with the federal members of Parliament."

Hobart City Council voted unanimously earlier this year to support same-sex marriage, while Launceston City Council rejected a similar motion.