Labor is expecting Barnaby Joyce to stir up trouble for the Turnbull government from the backbench alongside former prime minister Tony Abbott.

“They will be like Statler and Waldorf from the Muppet Show, the government’s greatest critics, trying to bring Malcolm Turnbull and the government down,” Labor frontbencher Jason Clare told ABC television on Sunday.

Mr Joyce will retreat to the backbench on Monday after he announced his resignation from the Nationals leadership on Friday, succumbing to weeks of fall-out over his relationship with a former staffer.

The outspoken MP has promised not to “snipe” from the backbench but Labor expects him to follow the example of Mr Abbott, who made a similar promise when he was rolled for the leadership by Mr Turnbull in 2015.

He has been a thorn in the government’s side since, repeatedly taking opposing views on various issues.

Mr Clare doesn’t believe Mr Joyce’s promise and expects him, like Mr Abbott, to sit on the backbench and “fester and agitate” to try and derail the government.

But Nationals MP Darren Chester – who was forced out of cabinet by Mr Joyce – said he believed the former deputy prime minister would keep his word and be an asset to government.

“I’ve known Barnaby for 10 years. I’ve known him to be a team player who wants to see regional Australia get ahead,” he told Nine.

“I’m sure he’ll be a positive influence on National Party from the backbench.”

Deputy Liberal Leader Julie Bishop was more restrained about her thoughts on Mr Joyce joining the backbench, saying he would be one of many backbenchers.

“They will make a contribution policy, they will make a contribution to the debate of ideas which we encourage in the Liberal-Nationals coalition,” she told reporters in Adelaide.