Some Tasmanian tenants have started receiving notices of planned rent increases since the end of the moratorium on increases on February 1, while rent arrears repayments will also restart.

When a question suggested that rents are "out of control" in Hobart and "getting worse in Launceston", Mr Gutwein said "that's a dangerous statement to make".

"There have been one or two examples where obviously there have been reasonably significant rental increases," he said.

"But at this point in time, we don't have the data to demonstrate that that's going to be a sector-wide issue."

Related: Tasmanian renter cops $72-a-week rent increase as moratorium finishes

When asked if the government could do more to stop rents increases above the consumer price index, and that rents in Hobart were starting at a very high base, Mr Gutwein described it as "a very broad statement".

"Again, what we'll do is we'll continue to work with those in the sector to ensure we've got an understanding of what the impact is moving forwards," he said.

"But as I've said, we've made transitional arrangements, and we'll continue to work with both landlords and tenants as this evolves."

The questions were prompted by concern from ShelterTas that the government's social housing construction plan lacked ambition and was putting more stress on the private rental market, and the Tenants' Union claiming it was already receiving concerns about rapid rent rises in the past two weeks.

The government extended the Rent Relief Fund and Landlord Support Fund until March 31, involving up to $14,000 of assistance per eligible tenancy.

IN OTHER NEWS:

The government paid $3.1 million to landlords and tenants, removing 86 per cent of rent arrears.

The latest Rental Affordability Indexed, released in December, showed Hobart was Australia's most unaffordable capital city for renters, while Launceston was seen as "mostly acceptable", apart from Legana, Kings Meadows and Youngtown which were also seen as unaffordable.

In Hobart on Wednesday, there were 33 rental properties with at least two bedrooms available for fewer than $400-per-week. One in Lenah Valley was $310, another in Montrose was $330 and the majority were between $375 and $400.

Of the 33, five were standalone houses, three of which were in Risdon Vale. The remainder were units.

There was also a range of one-bedroom options closer to central Hobart.

What do you think? Send us a letter to the editor: