Trust in the internet was broken with the live-streaming of the Christchurch mosque massacre, Scott Morrison wants to tell world leaders.

The prime minister hopes to rally support among his counterparts for the G20 to work on stopping terrorists and violent extremists exploiting the internet, and social media in particular.

He was moved by the attack in New Zealand, when an Australian man allegedly killed 51 Muslims at two mosques and wounded dozens more, to push for a global crackdown on the tech companies.

The coalition government, with the help of Labor, passed laws just before the federal election to make it a criminal offence for companies not to take down videos that show abhorrent violent content.

Mr Morrison will push in a formal session of the G20 in Osaka on Friday to move towards adopting a set of clear principles about what is expected from social media giants.

“Without trust in the internet, digitalisation cannot reach its full potential. It’s that trust that was broken in the wake of the Christchurch terrorist attack,” he is expected to say.

He intends to highlight the story of the youngest victim, three-year-old Mucad Ibrahim, and appeal to leaders from the places those killed were from – Africa, Asia and the Middle East – to act.

“Global leaders taking a stand for ambitious and concerted action should be the real legacy left by the horrific acts in Christchurch,” he is expected to tell the closed session.

“The most effective way to bring social media companies into line is working with other countries so the same high standards apply equally everywhere.”

He also plans to argue that leaders have a responsibility to make the internet safe, noting that several G20 countries are home to the platforms that host or support this violent content, while also allaying concerns it could be seen as censorship.

Mr Morrison discussed his initiative in meetings with Japanese Prime Minister Shinzo Abe and US President Trump on Thursday night.

He told Mr Abe he strongly appreciated the Japanese leader’s support in including it on this year’s G20 agenda.

Australia believes it has already won over Canada and France, and Mr Morrison intends to lobby others during formal bilateral meetings and informal chats over the two days of the summit.

The other main focus for Australia at the G20 will be Friday morning’s talks on trade and the global economy.

Mr Morrison warned earlier in the week Australia would not be a passive bystander to the US-China trade tensions.

He was able to follow up these remarks at a working dinner with Mr Trump, urging the president to strive for a deal when he meets Chinese leader Xi Jinping in Osaka.

Mr Trump was asked at the start of the dinner whether he recognised his “America first” policies, especially on trade, hurt allies like Australia.

“I think I can say very easily that we’ve been very good to our allies,” he told reporters, saying the Australian relationship was a good example.

Another aspect of trade tensions Mr Morrison hopes to address is the continuing push to update the World Trade Organisation’s rule book.

Australia is seeking to build on momentum from last year’s G20 and set a benchmark for future success so that the global trading system is in better shape, not worse, with economic projections being revised upwards.

Mr Morrison hopes to tell other leaders they all have to play a part in solving the problems.

“All of us in this room have a critical stake in ensuring our trading system works and is durable,” he intends to say.

“The system needs the confidence of its members and it is clear that is no longer the case. We can’t let that mean we slip into a further deterioration in key trading relationships and the collateral damage that would bring.”