Stuart Davie told the Otago Daily Times this afternoon his position had become "untenable", but he declined to comment further.
"I would rather not comment at this stage."
There has been disquiet in the local electorate branch since the departure of Gore office electorate secretary Glenys Dickson earlier this month after the "employment issue".
Her resignation was followed by Queenstown office secretary Barbara Swan, who is working out a notice period.
On Friday, Gore National Party branch secretary Maeva Smith refused to express confidence in the first-term MP, saying "I'd prefer not to answer that", but she declined to comment today when contacted.
Parliament's youngest MP, Mr Barclay's career prior to entering Parliament included a stint as a tobacco lobbyist.
Contacted for comment, Mr Barclay emailed the ODT, saying Mr Davie was a "passionate supporter" of the National Party.
"Stuart has been the National Party Clutha-Southland electorate chair since April 2013 and has worked tirelessly for the Party and the electorate during that time."
"I wish him all the best for the future.
"I look forward to working with the new chair, who will be elected in the next few weeks."
