The federal government will double the penalty for breaches of Australia’s youth social media ban to $99m, arguing tech companies are “not doing enough” to keep children off harmful social media sites.

And the eSafety commissioner, now investigating potential breaches of the law by Facebook, Instagram, Snapchat, TikTok and YouTube, will have its information-gathering powers strengthened under proposed further reforms.

“I’m heartened by the shift in conversation and the global momentum we’ve seen since introducing the social media minimum age,” the prime minister, Anthony Albanese, said, “but it’s clear big tech are not doing enough to comply with the law – there are still too many children on social media.”

The government said more than 5m accounts held by under-16s had been removed, deactivated or restricted since Australia’s world-leading ban was introduced on 10 December, but research suggested the majority of under-16s were bypassing age restrictions and still accessing social media.

The proposed new laws would double the penalty for systematic breaches of the under-16s social media ban – from $49.5m to $99m – bringing it into line with penalties available under competition and consumer law.

The reforms would also give the eSafety commissioner the power to compel social media companies to provide evidence of what they have done to stop under-16s from opening or using an account. The commissioner would be able to demand information and documents, including from third parties, such as age assurance or app store providers.

“Australia is leading the world in our efforts to keep kids and young people safe online,” Albanese said.

“These changes reflect the seriousness with which we take any failure by social media companies to comply with our world-leading law.”

Since Australia became the first country in the world to legislate a social media-ban for under-16s, international momentum for similar reforms has been growing.

The French national assembly had passed legislation to prohibit access to social media accounts for children under 15 – with provisions for parental consent – and the UK government had announced plans for an “Australia-plus” ban for under-16s from 2027, with additional restrictions.

Similar proposals were also being considered by Slovenia, Poland, Spain, Denmark and Malaysia.

But research evaluating the effectiveness of Australia’s ban found more than 80% of under-16s were still using social media, three months after the legislation came into force.

A study of more than 400 12- to 17-year-olds by the University of Newcastle concluded Australia’s social media minimum age legislation had resulted in “limited implementation, incomplete compliance, and substantial circumvention of social media restrictions”.

“Overall, we found insufficient evidence to conclude that exposure to the act [of parliament] had any early substantial effects on social media use among adolescents aged under 16 years,” the authors said.

The research, published in the BMJ this month, found that while two-thirds of teenagers in the study reported being asked to complete age verification checks, only 5% of 12- to 13-year-olds and 11% of 14- to 15-year-olds had to provide a photo of official ID. The two most common checks were asking teens their age or uploading a picture of themselves.

A significant minority of participants said they actively bypassed the age restrictions. About 15% of the 12- to 13-year-olds and 19% of the 14- to 15-year-olds surveyed said they used a fake account, while about 3% said they used a VPN.

The study argued the Australian social media ban may be more effective in preventing or delaying access to social media in children under eight, rather than restricting access to adolescents who already use it.

The communications minister, Anika Wells, said that after six months of operation of the social media law, she did not believe big tech companies were doing everything they could to exclude under-16s.

“Based on the regular updates I receive from the eSafety commissioner, it is clear to me that social media platforms are adopting tricks straight out of the big tech playbook and doing the bare minimum to get by.

“In response, I am making sure the regulator has stronger tools to get the job done and doubling the fines for non-compliance.”

She said social media platforms were some of the richest and most powerful companies in the world, but the government would not be deterred from ensuring the children’s social media ban was upheld.

“These tough new penalties and powers show we will not back down. Instead, we are doubling down on our efforts to hold big tech to account.”