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Nine councillors signed a copy of a letter requesting that a meeting be held on July 8 to discuss her possible removal.
The nine are Crs Hilary Calvert, Kevin Malcolm, Michael Deaker, Andrew Noone, Gretchen Robertson, Carmen Hope, Gary Kelliher, Kate Wilson and Michael Laws, the deputy chairman.
Crs Alexa Forbes and Bryan Scott and Ms Hobbs did not sign it.
The letter was delivered to council chief executive Sarah Gardner yesterday and the council confirmed last night an extraordinary meeting would go ahead on July 8, at 9am.
If Ms Hobbs is deposed, a replacement could be elected by a majority of councillors at that meeting.
The move to oust Ms Hobbs comes amid concerns by some councillors that she is too closely aligned with central government.
However, her supporters have pointed out regional councils are required to be largely in tune with national policy.
Cr Noone visited Ms Hobbs on Sunday morning to ask whether she would consider standing down.
"I was keen to hear where she was at.
It was important to have that discussion."
Ms Hobbs advised she would not step aside.
Cr Kelliher wrote to Ms Hobbs on Sunday, advising that a majority of councillors would seek her removal as chairwoman.
Ms Hobbs’ reply was to the point: "I was elected in public. I want to be de-selected in public."
Ms Hobbs, a former environment minister, was voted in as chairwoman last October.
She defeated former deputy chairwoman Cr Robertson 7-5.
Cr Laws was voted in as deputy after withdrawing from a tilt at becoming chairman.
Cr Scott said yesterday he would want to be convinced that any candidate to replace her would take the organisation forward.
"I need to be reassured that whoever puts their hand up will have a positive environmental vision for our region, and that we get on with it."