Michael McCormack says he has the “absolute solid support” of his party room and won’t be going anywhere, amid reports some Nationals are dissatisfied with his performance and are considering moving a spill motion to try to return Barnaby Joyce to the leadership.

“No National party member has come to me and said, ‘I’m dissatisfied with the job that you’re doing,’” the deputy prime minister told Sky News on Thursday. “They’ve come to me and they’ve offered me solid support.”

Speculation about the leadership flared on Wednesday after Joyce said he would take it if it were offered to him but denied suggestions he was “collecting the numbers” against McCormack.

The fresh Coalition leadership tensions come less than two months after Malcolm Turnbull was dumped as prime minister, and days before a crucial byelection in Wentworth.

McCormack was elected after Joyce stepped down in February after the fallout over his affair with a former staffer and now partner, Vikki Campion, and allegations of sexual harassment made by the rural advocate Catherine Marriott. A party investigation into the allegations was unable to make a determination, according to Marriott.

This week’s outbreak of leadership speculation follows continuing tension over proposed agricultural visas for foreign workers to fill seasonal farm jobs. The visa, which is a National party policy, is also supported by the National Farmers’ Federation, but Scott Morrison has moved to delay any visa and has instead urged farmers to report their short-term harvest employment needs to the National Harvest Labour Information Service.

Some in the National party consider this a failure of leadership on McCormack’s part; others say it was an issue for the agriculture minister.

McCormack was asked on Thursday if he could reassure his colleagues that he was taking it up to the Liberals on the agricultural visa issue. He said he was “absolutely rock solid behind” the Coalition’s policy on visas, as was his party room, because it served the interest of farmers.

He was also asked if he had misleadingly told his party room that the agricultural visa was part of the secret Coalition agreement.

McCormack replied: “I don’t tell people outside the party room or indeed outside cabinet [about] the Coalition agreement, I don’t tell the general public what goes on inside those arrangements, and nor will I.

“The fact is we’ve got arrangements in place to fill the labour workforce needs of the agriculture sector.”

The Liberal National party minister Michelle Landry – who is a supporter of Joyce – told Sky News on Thursday that McCormack had the support of the party room and ought to be given a fair go.

“I have spoken to a lot of my colleagues,” she said. “No one is interested in change of leadership, leadership challenges. We’re happy with Michael to remain as our leader.

“Barnaby is keen down the track to take over the leadership. And as he said, if it was offered to him, if Michael stood down, he’d be prepared to put his hat in the ring for that. But he certainly hasn’t been going around doing the numbers.

“I think that Michael needs to have a fair go at this. We’ve just seen a change in the leadership of the Liberals and I do not think people want us talking about ourselves again. So I think that everyone just needs to calm down on this.”

Landry claimed none of her colleagues were talking about the leadership tensions.

“I’m with the federal Nationals. My colleagues aren’t talking about this. The only one that’s really talking about it is the media.

“I’m sure at some stage in his career Barnaby will be the leader again. But Michael is our leader now, he has the support of the party room, and I have spoken to quite a few of my colleagues about this and they are all very supportive.

“Now is Michael’s time. I think that Michael is doing a great job. He’s been up to my electorate quite a few times. He resonates well with the people up there. And I think that people need to give him a fair go.”