Last month, the Tenants' Union of Tasmania wrote to Housing Minister Roger Jaensch requesting he reopen with urgency 20 cases where social housing tenants were evicted without being afforded procedural fairness.

The letter follows a Supreme Court decision which ruled social housing tenants could only be evicted for "genuine or just" reasons, not simply because their lease was due to expire.

The union sought Mr Jaensch reopen the matters of 20 tenants who were evicted on this basis during the time the Supreme Court appeal was underway, from the date the appeal was filed on October 18, 2017.

Mr Jaensch confirmed in Parliament question time on Tuesday the Director of Housing did not intend to review the matters.

Mr Jaensch said the cases in question had been appropriately determined by the courts.

"No further action is deemed to be warranted," Mr Jaensch said.

Mr Jaensch said Housing Tasmania had a three strikes approach in regards to evictions.

"This approach gives tenants the ability to rectify any breaches of tenancy agreement with the point of avoiding notices to vacate," he said.

"Evictions are always a last resort

"A notice to vacate only occurs if a tenant seriously and repeatedly breaches their tenancy agreement."

Greens leader Cassy O'Connor said the eviction cases should be reviewed.

"We should have had a commitment from the minister that no more Housing Tasmania tenants would be evicted just because their lease has expired," Ms O'Connor said.

"It is the role of Housing Tasmania to be a model landlord and look out for vulnerable tenants."