Barnaby Joyce does not have the “sober and sensible approach” required to become deputy prime minister, the acting opposition leader, Penny Wong, has said.

Wong labelled Joyce, who has reiterated his desire to become the next leader of the National party, “entertaining but erratic”.

The position will become vacant with the widely anticipated imminent retirement of the Nationals’ leader, Warren Truss.

“I’ve supported Warren publicly and privately and if he steps down I will throw my hat in the ring,” Joyce told Fairfax Media on Thursday.

A spokesman for Joyce, who is on leave, told Guardian Australia the agriculture minister was not agitating for a leadership spill, and would put his hat in the ring only when Truss stood down.

“In the event of that happening, he will put up his hand,” the spokesman said.

Wong said the prospect concerned even some of Joyce’s colleagues.

“He simply doesn’t have the sober and sensible approach to public policy that Australians expect from the holders of high office,” Wong said. “Even Barnaby’s own colleagues are worried about him taking on this role.”

The leader of the National party holds the deputy prime ministership, and takes on the top job when the prime minister is overseas or on leave.

“We all remember Barnaby being shadow finance minister. That was certainly entertaining, but if he can’t hold down that job, I don’t know how you hold down the deputy prime ministership,” Wong said.

Joyce’s spokesman said criticisms of the minister were historical in nature and did not take into account the good work Joyce had done with the agriculture portfolio.

“Agriculture has been elevated to a key ministry [under Joyce],” the spokesman said.

But Wong argued having Joyce “out campaigning” for the job had a “destabilising” effect on the government more broadly.

“It’s not the sort of stable government I think Australians want. We’ve had a lot of division on display over this Christmas/new year break, and now Barnaby has simply added to it,” she said, referring to the resignation of Jamie Briggs and the announcement that embattled minister Mal Brough would stand down while a police investigation into him continued.

A wholesale ministerial reshuffle to fill the vacancies left by Brough and Briggs is not expected until after Truss resigns.

The foreign affairs minister, Julie Bishop, has given Joyce a rap over the knuckles for speaking out before the position had officially become vacant.

“Warren Truss is the leader of the National party and he is the deputy prime minister,” she told ABC radio on Thursday.

“Warren is a very dear friend and a good colleague so I think out of respect for Warren, we should allow him to make a decision as to his future before we start talking about his successor.”

Bishop would not be drawn on who she thought should lead the party.

“The leadership of the National party is a matter for the National party. Barnaby is the deputy leader and is doing a very fine job but the question of the leadership of the National party – given that it brings with it the deputy prime ministership – is obviously a significant matter for the National party to determine,” she said.