A moratorium on evictions for rent arrears and the prohibition of rent increases will end on September 30, while the federal government plans to reduce both JobKeeper and the coronavirus supplement by $300 per fortnight at the same time.

The letter, co-signed by the Tenants' Union of Tasmania, Shelter Tasmania, Community Legal Centres Tasmania, Anglicare Tasmania and TasCOSS, outlines fears for 39,500 Tasmanians on JobSeeker who could face poverty.

"If protections for residential tenants are not extended beyond 30 September 2020 there is a high likelihood of evictions for people who, through no fault of their own, have lost their jobs and are struggling to pay the rent," the letter reads.

"It will also result in rent increases for tenants who simply cannot afford any rent increase at this time."

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The organisations cite the Australian Bureau of Statistics' COVID-19 economic vulnerability index which showed the most vulnerable areas were in capital cities and regions reliant on tourism.

In Tasmania, Launceston and north-west Hobart were considered the most at-risk areas in regards to the economic impact of COVID-19. Mowbray was considered most at risk, followed by Invermay and Ravenswood.

The five organisations also called on the government to provide further payments of up to $2000 - or four weeks' rent - through the residential rent relief scheme, available to those who could demonstrate financial hardship.

"A further payment ... will act as an important protection for residential tenants in their continued efforts to keep up with their rent whilst ensuring that landlords are assured continued rent payments," the letter reads.

Based on the latest real estate data, tenants living in houses in Hobart were using more than 100 per cent of their JobSeeker payment on rent, while Launceston tenants were using 76 per cent.

On Wednesday, the Greens attempted to add an amendment to extend the rental protections to a motion from Labor which called for a winter energy supplement. The amendment was not supported, but Labor had earlier questioned the government about extending rental protections.

Both parties have put their support behind extending the protections for renters.

Earlier this week, Building and Construction Minister Elise Archer said the government was closely monitoring economic conditions and would make a decision on rental protections before the end of September.