Australia's federal government stepped up pressure on state and territory leaders on Friday to reopen internal borders while some parts of the country have effectively eliminated the deadly coronavirus, which was seen as a vital step to revive the country's coronavirus-hit economy.

Australia has eliminated the novel coronavirus in many parts of the country, its chief medical officer Brendan Murphy claimed on Friday.

Australia's Prime Minister Scott Morrison plead at a meeting of the national cabinet dealing with the crisis, just hours before protesters are expected to defy movement restrictions for a Black Lives Matter rally in Sydney.

Morrison last month announced a three-step plan to remove the bulk of lockdown measures by July, which would allow for domestic travel. With case numbers falling significantly, Morrison said restrictions on indoor gatherings would be loosened in July with crowds of up 10,000 people allowed in seated stadiums and a trial scheme to allow foreign students to return.

But the implementation of the federal plan is down to the leaders of individual states and territories, who come from opposing political parties and disagree on how safe it is to lift restrictions.

Australia's Finance Minister Mathias Cormann told Sky News on Friday that the state borders should be open, adding that a second wave of infections could cost the economy 80 billion Australian dollars over the next two years.

But the pathway out of lockdown has been complicated by rallies to support the Black Lives Matter movement. Morrison said gatherings last weekend that attracted tens of thousands had delayed the process.

The movement has refocused attention in Australia on the mistreatment of indigenous Australians, including Aboriginal deaths in custody. A rally is scheduled in Sydney on Friday despite warnings of on-the-spot fines and arrest and more are planned.

Morrison drew criticism on Thursday for saying "there was no slavery in Australia" during a discussion of the early days of British settlement.

Australia recorded just 38 coronavirus cases over the past week, and has 7,289 cases and 102 deaths overall according to Johns Hopkins University.

(With input from Reuters)