Scott Morrison faces calls from within government ranks to extend the increase to unemployment benefits until at least next year amid fears the outlook for jobseekers will remain bleak on the other side of the coronavirus crisis.

While the prime minister has insisted a raft of crisis-related economic support measures will “snap back” to their old arrangements to avoid an ongoing budget drain, social welfare advocates argue the jobseeker allowance can never revert to just $40 a day.

The Nationals MP for Cowper in NSW, Pat Conaghan, said the effective doubling of the allowance formerly known as Newstart should continue well beyond the six-month deadline.

“My priority is to ensure all people during this challenging time who are losing hours of work or losing jobs have support and I would like to see the coronavirus supplement extended for a further six months to do this,” he said.

“Many people who weren’t previously on Newstart and who have lost their job due to the effects of Covid-19 may still struggle to find a job in the six to 12 months after the pandemic, so I would like the coronavirus supplement safety-net extended.”

After that, Conaghan said, jobseeker may have to be reduced to begin the task of budget repair but not to its previous levels. He suggested that the weekly rate should be about $75 to $95 above the old rate of $280 per week.

The coronavirus supplement that tops up certain income support payments is due to begin flowing from next week.

The government has so far processed more than 587,000 jobseeker and related applications since mid-March, more than it normally handles in a year, Morrison said this week.

But when asked whether the government was open to considering an increased payment for jobseekers for longer than the six months, the prime minister said: “We’ve put a Covid supplement in place for the period of the pandemic and that’s what we’ve budgeted for and that’s what our policy is.”

That was despite his comments in the context of economic reform that policy ideas needed to be looked at with “fresh eyes” once the crisis subsided.

Former prime minister Tony Abbott joined the fray on Friday, arguing it would be politically difficult for the government to wind back the increased jobseeker allowance, “especially when recipients will be able to say it was government policy that threw them out of work”.

Writing an op-ed in The Australian, Abbott suggested turning the payment into “a wage subsidy for older people and a part-time environmental job with local government for younger people”.

The opposition leader, Anthony Albanese, said the Coalition had increased the jobseeker amount because it admitted $40 a day wasn’t enough to live on.

He said: “If it wasn’t enough to live on two months ago, when these changes were made, why will it be enough to live on in six months’ time?”

Quick Guide How to get the latest coronavirus news from Guardian Australia Show Email: sign up for our daily coronavirus newsletter App: download it and never miss the biggest stories Social: follow us on Facebook, Instagram or Twitter Podcast: listen to our daily episodes on Apple Podcasts, Spotify or search "Full Story" in your favourite app

Labor’s social services spokesperson, Linda Burney, said the government should take the opportunity to set a higher, fairer base rate as it was “unrealistic to think income support can go back to its $40 a day rate without causing hardship to the hundreds of thousands of Australians out of work”.

Cassandra Goldie, the chief executive of the Australian Council of Social Service, said one of the best ways to support the recovery would be to continue to provide income support and cash stimulus to people who needed it, as people on low incomes would spend the money in the real economy.

“Now is the time for us to come together behind people hit hardest by this crisis, with so many now unemployed, and give them confidence that they will be supported with decency, and for as long as it takes,” she said.

Innes Willox, the chief executive of the Australian Industry Group, said the economic impacts of the crisis would be longer lasting and he called on the government to show flexibility when reviewing the situation in the months ahead.