A Tasmanian local government councillor's motion to end Welcome to and Acknowledgement of Country ceremonies at Council events has been resoundingly rejected.

Flinders Island councillor Garry Blenkhorn put forward the motion on Wednesday to abolish such ceremonies at council events, with Mr Blenkhorn's suggestion failing to gain a seconder.

The motion had not been discussed by council prior to the meeting, nor had the local community - which has the second highest proportion of Aboriginal people in Tasmania - been consulted.

Flinders Island Council's meeting was attended by approximately 50 people on Wednesday, including many from the local Aboriginal community, and was also streamed online.

In the public gallery was Cape Barron Island Aboriginal Association representative Denise Gardner, who clapped and cheered as the motion failed.

"We were quite elated but not surprised at the outcome," Ms Gardner said, the ABC reports.

"We had half a dozen people fly over from Truwana Island to attend and had people on Skype watching the proceedings."

Ms Gardner said the motion "shouldn't have even been put on the table," while criticising its timing - during National Reconciliation Week.

"It's just amazing that it would be a motion at what is quite a sensitive time for people when we're all trying to go forward," she said.

"Flinders Council have done a lot of work with communities on Flinders and Truwana/Cape Barron to get work together, get on with business and work together on common causes and for the best part that has been happening.

"We move forward on that."

Speaking at the meeting following the motion's defeat, Flinders Island deputy mayor Vanessa Grace criticised the process undertaken by Cr Blenkhorn.

"While Cr Blenkhorn says he is representing up to 100 people's views and he's brought them all forward, such a significant change should have been brought to council for a workshop, discussion and collaborations with the community and the key stakeholders, the Aboriginal communities," Ms Grace said.

"This … has caused much angst and division."

Flinders Island mayor Rachel Summers said it was "a good move" for the motion to not be supported, but said it had caused damage regardless.

"Councillors spoke out in support of our community rather than the motion, so it was really good to see that," Ms Summers said.

"Unfortunately, damage has been done out of this and I really hope council can work with our Aboriginal community, with the organisations that represent those communities and find a way to walk forward together."

Mr Blenkhorn said there had been "an increase in discontent throughout Australia" for Welcome to and Acknowledgement of Country ceremonies, saying he believed such ceremonies had "served their purpose".

"The use of Welcome to Country and Acknowledgement of Country is seen as divisive, unnecessary and not contributing to reconciliation between Indigenous Australians and others," Mr Blenkhorn wrote in his report for putting forward the motion.

"I believe the two protocols have served their purpose and it is now time to move on."