The Greens' party room says Richard Di Natale is safe as leader, but a senior figure from the West Australian branch wants him to resign.
Federal Greens also say infighting played a key role in the failure to win the Batman by-election on the weekend.
Former ACTU boss Ged Kearney defeated bookmakers' favourite Alex Bhathal on Saturday night to keep the seat in Labor hands.
Senator Di Natale said he would not resign over the loss and was supported by SA Senator Sarah Hanson-Young.
"Richard Di Natale's leadership is safe and we need him now, we need him to step up and make sure the party is pulled together tightly," Senator Hanson-Young told Sky News on Monday.
"Many of us here in Canberra are up for re-election ... we need Richard fighting for us and leading us strongly."
But three-time co-convenor of the WA Greens, Grahame Bowland, says it's time for Senator Di Natale to quit.
"Since Richard's appointment as federal parliamentary leader, untold cultural damage has been inflicted upon our movement," Mr Bowland posted on Facebook on Monday.
"We are now a party which, instead of embracing dissent, fears it, and reflexively acts against it."
Senator Di Natale blamed Labor's campaign machine and internal Green leaks for the loss of Batman, in Melbourne's inner north.
"We had a big Labor machine against us, corporate money, the significant support of the union movement - it was always going to be tough," he told ABC radio on Monday.
"It's very difficult to run a campaign when you're not just fighting a machine like that, but you're also fighting some of your own people."
Ms Bhathal's campaign for the marginal seat was rattled when a number of her branch members leaked details of bullying complaints against her.
She denies the allegations and an internal review is underway into how the leak occurred.
"Those people who are found to be responsible for leaking and undermining our candidate need to be expelled," Senator Di Natale said.
But Mr Bowland said it wasn't the first time the leader had suppressed dissent, and wouldn't be the last.
"We would have to be fools to think that Richard's call for a purge is in any long term sense limited to those allegedly responsible for the alleged leaks in Batman," he said.
The Liberal Party did not run a candidate in the by-election, which was called after sitting Labor MP David Feeney resigned over his dual citizenship.