Cr Bourke this afternoon "wholly denied" the allegations made against him on ABC TV's 7.30 program on Thursday night.

In the program, Councillor Jacqui Rudge alleged Cr Bourke had played a role in an attempt to blackmail her into resigning from Bathurst Regional Council in March 2020.

In a statement to the media on Friday afternoon, Cr Bourke said he would step down as mayor, effective immediately, in the wake of the program's allegations.

Deputy mayor Ian North will take on the role of acting mayor until councillors hold an extraordinary meeting within the next 14 days to elect a new mayor.

"In light of yesterday's ABC article and allegations against me, I have decided to step down immediately as mayor of Bathurst Regional Council," Cr Bourke said.

"The allegations in the report are levelled against me, and not any other BRC councillors.

"I believe that my stepping down is in the best interests of the people of the Bathurst region and all concerned."

Cr Bourke did not expand on the allegations levelled against him, saying the matter remained the subject of a police investigation.

The 7.30 program on Thursday night alleged Cr Bourke had asked a volunteer at the community op shop he runs, Chris Hosa, to write Cr Rudge's name and address on an envelope that was sent to her containing a typed blackmail letter in March 2020.

The letter threatened to expose Cr Rudge's "mental health issues" unless she resigned from council.

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According to 7.30, Cr Bourke "provided a statement to police confirming Hosa's account". Cr Bourke, who is self-isolating after a trip to Sydney last week, did not directly address that allegation in today's statement.

"The event referred to on the ABC program last evening occurred some 18 months ago; the allegations against me of bullying and threatening are wholly denied and are the subject of a police investigation," Cr Bourke said.

"I will remain as a serving councillor until the upcoming local government election on the 4th of September and then let the people decide.

"In the meantime, I will continue to act in the best interests of our Bathurst Regional Council and our community."

Council general manager David Sherley confirmed Cr Bourke had tendered his resignation.

"I have this afternoon received advice from Cr Bobby Bourke that he has resigned as mayor of Bathurst, effective immediately," Mr Sherley said.

"He has advised that he will remain as a serving councillor through until the September local government elections.

"Deputy mayor Ian North takes on the role of acting mayor from this afternoon following Cr Bourke's decision."

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