Josh Frydenberg has warned it is “very dangerous and unrealistic” to move ahead of medical advice, as Australian governments ponder trials of easing Covid-19 restrictions.

Appearing on ABC’s Insiders on Sunday, the federal treasurer predicted a “significant’ increase in unemployment as a result of coronavirus and said the government had “no plans” to change the GST, suggesting that growth alone might be sufficient to pay down debt incurred for $214bn of economic support packages.

Earlier, the deputy prime minister, Michael McCormack, sounded less optimistic, warning that the economic recovery “is going to need” tax reform and refusing to rule out GST changes.

On Sunday Australia’s death toll from Covid-19 rose to 58 and confirmed cases lifted to 6,289, as government authorities thanked Australians for staying home at Easter to consolidate a promising fall in the daily number of new cases.

The chief medical officer, Brendan Murphy, told reporters in Canberra there “is no place in the world I would rather be than Australia at the moment” but we should not be “complacent” due to ongoing community transmission.

With the rolling average of new case numbers below 2% for five consecutive days, states including Western Australia and New South Wales have already begun to suggest restrictions could be eased.

The NSW chief medical officer, Kerry Chant, has suggested a “zigzag” approach that could see restrictions on going outdoors for non-essential purposes eased on a trial basis then reinstated if case numbers increase.

Murphy noted that “around the world [countries] have released restrictions and have had to reimpose them” and said national cabinet would not lift restrictions until there are measures including surveillance and tracking to ensure case numbers stayed under control.

“But there is a huge risk in doing so and we have certainly said that it is not the right time now.”

Earlier, Frydenberg told Insiders it was “very dangerous and unrealistic to move ahead of the medical advice”.

“As the prime minister has said, patience is a virtue, and complacency is a problem,” he said. “And everyone needs to understand that this is a very fluid and difficult situation.”

Frydenberg noted that Scott Morrison had “prepared the nation for six months at least” of Covid-19 restrictions and would not predict if they could be lifted sooner.

“Again, I don’t have a crystal ball … We are having a degree of success in flattening out that curve.”

Frydenberg said he believed Australia would suffer a “significant increase in unemployment” due to the “severe economic impact of health restrictions” but business leaders understood the need to follow the medical advice.

Frydenberg revealed that 802,000 businesses had applied to access the jobkeeper wage subsidy for millions of employees, while more than 600,000 workers had applied for early access to their superannuation on the basis of financial hardship.

He suggested the number of those wanting access to super may shrink, as many had expressed interest before the $130bn wage subsidy program was announced and passed parliament.

The treasurer said the government had “no plans” to expand eligibility for the $1,500 fortnightly payment, explaining that a discretion for him to do so without recalling parliament was designed for “unforeseen circumstances”.

The Australian Council of Trade Unions and Labor have cited the treasurer’s discretion as the basis for an ongoing campaign for one million casuals with less than 12 months service with their current employer and 1.1 million temporary visa workers to get the payment.

Frydenberg revealed it would cost $18bn to add one million casuals to the program, but insisted he intended to use his discretion only “if you needed to implement [the program] in a different way with the [Australian Tax Office]” if issues arose in the implementation phase.

Frydenberg said shorter-term Australian casual workers would be eligible for the $1,100 fortnightly jobseeker payment instead, while temporary visa-holders could access their superannuation, continue to work or return home.

“At $130bn … we had to draw the line somewhere. This is a massive call on the public purse and it is a debt that the country will pay for years to come and at six million people on the jobkeeper program, that’s nearly half the Australian workforce.”

Asked if tax increases would be needed to pay back fresh debt, Frydenberg replied that “it will be paid back in the years ahead”.

“But, again, we approach this crisis with about a quarter of the debt to GDP ratio of the US, of the UK, and about one seventh of what it is in Japan.

“The way to meet that growing debt burden will be to grow the economy.”

Frydenberg said the Liberal party is “the party of lower tax” and claimed its track record showed it could restrain government spending. “We are going to have to climb that mountain again.”

Frydenberg talked tough about the need to fight Covid-19, which he described as a “faceless and flagless enemy” but warned that – despite the prime minister’s call to protect Australia’s sovereignty – the current crisis is “not an argument for protectionism”.

Earlier, McCormack said “the recovery out the other side is going to need that [tax reform]”.

“I think the expenditure review committee and the states will be having a large say in that,” he told Sky News.

McCormack claimed the Coalition knew how to “manage money” but said the federal government would “need the help of Labor states and territories, through the [Council of Australian Governments] process and the national cabinet being its best self” to manage tax reform.

On Sunday the education minister, Dan Tehan, guaranteed that the federal government will pay $18bn in commonwealth grant scheme funding to universities this year regardless of whether they meet the student numbers estimated at the time of the 2019 budget.