Labor remains ahead of the Morrison government as the major parties gear up for budget week and the looming federal campaign, and, in the wake of the Christchurch murders, 63% of voters believe white extremism is as dangerous as Islamic fundamentalism.

With Scott Morrison due to meet executives from social media companies on Tuesday, a strong majority of voters in the latest Guardian Essential survey believe social media companies should not be allowed to broadcast violent material on their platforms.

The Morrison government is considering new laws that would make it a criminal offence if social media companies fail to quickly remove footage broadcast on their platforms in instances like the violent Christchurch attack – the worst mass shooting in New Zealand’s history. The laws are modelled on existing offences requiring social media companies to notify police of child abusers on their sites, and take down offending material.

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Ahead of Tuesday’s meeting, Morrison said: “We need to prevent social media platforms being weaponised with terror content.”

“If social media companies fail to demonstrate a willingness to immediately institute changes to prevent the use of their platforms, like what was filmed and shared by the perpetrators of the terrible offences in Christchurch, we will take action,” the prime minister said.

With the New South Wales state election now resolved, and with the federal campaign only weeks away, the latest Guardian Essential poll puts Labor ahead of the Coalition on the two-party preferred measure 52% to 48%, which compares with 53% to 47% a fortnight ago.

The positive movement inside the margin of error in the Coalition’s favour over the past fortnight reflects a softening of Labor’s vote in NSW, which likely reflects the impact of the state poll won by Gladys Berejiklian.

In NSW, the Coalition’s primary vote went from 39% during the last survey to 41%, with the poll in the field over the election period.

In the latest survey of 1,085 respondents, the Coalition’s primary vote nationally is on 39% (up two points in the fortnight), Labor’s primary vote is on 36% (down two points), the Greens are on 10% (up two points), One Nation is on 7% (steady) and others and independents are on 8% (down two points).

Voters were asked in the latest poll about their impressions of the Christchurch tragedy that has dominated the headlines over the past fortnight, and about their expectations for the budget on 2 April.

A majority of the sample (69%) believed social media platforms should be forced to ensure violent material is not broadcast through their sites, with strong support for that across all voting groups – and 63% agreed with the statement white extremism is every bit as dangerous as Islamic fundamentalism, again with strong agreement among Labor, Coalition and Greens voters.

Just under half the sample, 49%, believed that television networks and mainstream media outlets that have provided platforms for people with extreme and racist views need to bear some responsibility for the attack, with women slightly more likely than men to hold that view.

With Christchurch also prompting a public debate about race politics, just under half the sample (42%) agreed with the statement “politicians from Australia’s major parties have deliberately stirred up anti-Islamic sentiment as a way of getting votes”. Men were slightly more likely than women to think that, and Greens and Labor voters were more likely to think that than Coalition voters.

About the same proportion, 40%, thought Christchurch was an isolated act of evil rather than being connected to any broader debates, and 37% of the sample reported hearing racist or Islamaphobic statements regularly in their lives.

New Zealand’s prime minister, Jacinda Ardern, gets a powerful thumbs-up from Australian voters, with 71% of the sample reporting their views of her are favourable – compared with Morrison, who on favourability only rates 41%. Morrison is, however, ahead of Angela Merkel, Theresa May and Donald Trump (who gets the thumbs-up from only 19% of the sample).

Coming to expectations about the Morrison government’s pre-election budget, a majority believes next Tuesday’s economic statement will be good for people who are well off (58%) and half of the sample think it will benefit business.

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Even though the government has been telegraphing tax cuts targeting low and middle income earners and a big infrastructure spend, only 19% of the sample think they will personally benefit, and 34% suspects next Tuesday’s budget will be bad or very bad for them.

That expectation level is similar to where voters were before the Coalition’s 2018 budget, when 18% thought it would deliver personal improvements. The year before, only 8% thought the budget would be good for them.

Coalition voters are slightly more positive, with 29% of the cohort thinking they will have a good budget compared with Labor supporters (18%), Greens (13%) or people intending to vote for an other independent/minor party (8%).

A majority of voters want more spending in health, education and aged pensions. Business tax cuts remains unpopular, and only 11% of the sample wants the aid budget increased.

All voting cohorts want more spending on health. Labor and Greens voters are more inclined than Coalition voters to want to increase the spend on education and pensions.

Coalition voters are less supportive than Labor and Greens voters about increasing spending for renewable energy (39%), environmental protection (32%) and providing assistance to the unemployed (27%).

Voters at the moment are more worried about health care and cost of living pressures than job security.