Three Nationals senators have resigned from the frontbench after they crossed the floor to vote against Labor’s hate speech bill.

Sussan Ley accepted the trio’s resignation on Wednesday, a day after Ross Cadell, Bridget Mckenzie and Susan McDonald voted against the Coalition’s position on the contentious legislation, a breach of shadow cabinet solidarity rules.

It is the latest challenge to the authority of Ley, and the Nationals leader, David Littleproud.

Convention requires frontbenchers to vote in line with shadow cabinet’s decision or resign their role on the frontbench.

In a statement released on Wednesday, Ley said shadow cabinet solidarity “is not optional”.

“When the Coalition reformed in May last year, the foundational principle underpinning that agreement was a commitment to shadow cabinet solidarity,” the statement read.

“Yesterday, in several conversations, I made it clear to David Littleproud that members of the shadow cabinet could not vote against the shadow cabinet position … this is an unfortunate circumstance and one that requires action.”

Ley said she has asked Littleproud to nominate three other Nationals to join the frontbench.

Earlier, multiple senior Coalition sources confirmed to Guardian Australia that Nationals MPs had discussed a “one-in, all-in” approach in which all of their shadow ministers – including Littleproud – quit the frontbench if Ley sacks the three senators.

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One Liberal MP told Guardian Australia it was “disappointing” the Nationals were considering a mass walkout but said Ley should reject the offers to resign.

“The Nats all resigning en mass turns a story about an own goal by Albanese into a Liberal party story … she should keep them and let’s move on,” they said.

Littleproud and other Nationals frontbenchers in the lower house abstained from the vote, which was also technically a breach of shadow cabinet’s position to work with Labor to pass the bill.

Coalition sources confirmed the Nationals did not object to the position agreed at shadow cabinet on Sunday night, with the country party’s position only hardening on Monday afternoon.

The Nationals held another party room meeting on Wednesday morning, amid anger at the trio and backbencher Matt Canavan, who also voted against the bill. As a backbench MP, Canavan is not bound by shadow cabinet solidarity rules.

One Nationals source described the party room meeting as focused on “pastoral care”.

The Liberal leadership group, including Ley and her Senate leaders, Michaelia Cash and Anne Ruston, also held crisis talks on Wednesday morning.

Earlier on Wednesday, Cadell said he was willing to go to the backbench if requested by Ley, but stood by his decision to cross the floor.

“I understand if you do the crime, you have to do the time, and if it is so requested, I will be stepping down from shadow cabinet,” he said. “I am willing to take my medicine.”

The legislation, which will allow the government to designate organisations as “hate groups”, gives the home affairs minister additional grounds to cancel or reject visas and introduces tougher penalties for religious and spiritual leaders who promote violence, passed the Senate 38 to 22 votes after 11pm.

The Liberal frontbencher Dave Sharma told Channel Nine the trio should have voted with their Coalition colleagues.

“I was disappointed to see that. And it didn’t reflect the understandings that had been reached,” he said.

“From my perspective it’s important that we helped the government pass these important laws to allow us to take tougher action against people inciting hatred.”

The Coalition briefly split after the May election, after the National party had tried to strong-arm Ley into signing on to a deal that would make nuclear policy, a regional future fund and powers to break up supermarkets part of the Coalition’s policy platform.

The two leaders returned to the negotiating table in 48 hours, and the Coalition reunited one week later.