Laws to ban hate groups and establish a national gun buyback scheme have passed the Senate after the Albanese government struck separate deals with the Liberals and Greens to legislate its response to the Bondi beach massacre.

The two bills were rushed through on Tuesday night at the end of a special two-day sitting to deal with the political fallout to the 14 December shooting.

The hate speech laws divided the Coalition, with the Nationals splitting from the Liberals to oppose what the Nationals leader, David Littleproud, described as a “mess” that “overreached”.

With Littleproud watching on from the Senate chamber, the Nationals senate leader, Bridget McKenzie, accused the government of “trashing the normal process of parliamentary scrutiny in a vain attempt to secure a fleeting political win”.

After several of their amendments were rejected, the four Nationals senators joined the Greens, One Nation, David Pocock, Fatima Payman, Tammy Tyrrell, Ralph Babet and Liberal Alex Antic in opposing the bill, which passed 38 votes to 22.

In a statement, Littleproud said the country party’s decision, which was reached after more than half a dozen party room meetings across Monday and Tuesday, “does not reflect on the relationship” with the Liberals.

The split occurred despite shadow cabinet – of which Littleproud and McKenzie are members – resolving on Sunday night to thrash out a deal with Labor.

The laws allow the minister to ban hate groups, including neo-Nazis and Islamist organisation Hizb ut-Tahrir, increase penalties for so-called hate preachers who advocate or threaten violence and expand powers to revoke or refuse visas for people with extremist views coming to Australia.

After Ley last week described the original bill as “unsalvageable”, Liberal MPs agreed to support its passage after Albanese dropped the contentious anti-racial vilification provision and accepted several other amendments.

The changes include expanding a new aggravated offence for hate preachers to also capture guest speakers, requiring two-yearly reviews of the laws by parliament’s Joint Committee on Intelligence and Security and ensuring the opposition leader is consulted on both the listing and de-listing of hate groups.

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New rules to ban extremist organisations would target those who seek to incite violence, Ley said.

“In the national interest, the Liberal party has today stepped up to fix legislation that the Albanese government badly mishandled,” Ley said in a statement.

“We have succeeded in narrowing the scope of this bill to deal with what we said it should do – tackle antisemitism and tackle radical Islamist extremism.”

Liberal MPs who were critical of the original bill, including Andrew Hastie, eventually supported it after Ley secured the changes. Explaining his position in a video to supporters, Hastie said the new visa cancellation powers and banning of hate groups were worth supporting.

“Last week, Labor presented a bill which was terrible. We gutted it like a fish. What was left was some significant changes,” he said in a video posted to Instagram.

The Greens opposed what it described as “anti-association” legislation, warning it went even further than the original version in threatening the rights of people to call out the actions of other countries.

“This terrible deal between Labor and the Coalition will have a chilling effect on political debate, protest, civil rights, and people speaking up about civil rights abuses across the world. The Greens will vehemently and strongly oppose this bill,” the Greens antiracism spokesperson, Mehreen Faruqi, said.

The home affairs minister, Tony Burke, dismissed the Greens’ concern.

“I don’t believe that that’s possible in any way, shape or form,” Burke told ABC’s Afternoon Briefing when asked if the laws might silence legitimate criticism of other countries.

Burke rejected assertions the changes would impinge on freedom of speech, saying only they would only have a “chilling impact on racist bigotry”.

“I don’t accept that racist bigotry is within the free speech domain,” he said.

Appearing on ABC’s 7.30 program on Tuesday night, the attorney general, Michelle Rowland, confirmed a group could theoretically be banned under the new regime if it accused Israel of genocide and rejected its right to exist and as a result Jewish Australians felt harassed or intimidated.

But Rowland said other criteria, including breaching relevant state laws dealing with racial vilification, would also have to be met.

The home affairs minister would list an organisation based on advice from the Australian Security Intelligence Organisation (Asio), which must be satisfied that the group’s activities would increase the risk of politically motivated violence or the promotion of communal violence.

The Greens provided the numbers for the government to pass separate gun laws, which establish the largest national gun buyback since the 1996 Port Arthur massacre, introduce more rigorous background checks for gun owners and impose new import controls.

The Nationals unsuccessfully pushed for several amendments before joining with the Liberals to oppose the bill, which they characterised as an unjustified attack on law-abiding gun owners.

The passage of the laws follows Albanese’s decision to announce a royal commission into antisemitism after initially resisting calls for a national inquiry, including from families of the Bondi victims.