More than 33,000 asylum seekers already in Australia could be able to apply for permanent visas if a new high court challenge succeeds – thwarting ongoing attempts by the Abbott government to ensure no boat arrivals can stay permanently.

The latest challenge, brought on behalf of a Rohingya man by the Fragomen law firm, is one of three now before the high court, but has the much broader potential impact of paving the way for all asylum seekers already in Australia to make a claim for a permanent protection visa.

The other two cases, one brought on behalf of an Ethiopian boy, and another on behalf of a Pakistani man, would mean around 4,000 asylum seekers who had previously had a ministerial “bar” lifted to allow them to claim asylum could now claim permanent protection.

If the Senate disallows a last-minute regulation made by the minister after parliament rose last year – as would appear likely after it returns on February 11 – that would also pave the way for the 4,000 or so to claim permanent protection.

But a new challenge was lodged on January 6 on behalf of the stateless Rohingya man who was born in Burma and who arrived in Australia in 2011 and remains in immigration detention.

If it also succeeds it could mean around 33,000 asylum seekers who have already arrived in Australia by boat could make a valid claim for a permanent protection visa.

“If both of our clients ... (the Pakistani man and the Rohingya man) receive decisions from the high court which are favourable to them, there is the possibility that unauthorised maritime arrivals will not be denied the opportunity to apply for and be granted protection visas, simply for reason of being unauthorised maritime arrivals,” Fragomen special counsel Farid Varess said.

Immigration minister Scott Morrison insists the government has a “thumping mandate” to restore temporary protection visas and that denying any chance of permanent protection for those asylum seekers already in Australia is “as important as ensuring that those who now seek to come are denied settlement … by being sent to Nauru or Manus Island” for the government to achieve its aim of “stopping the boats”.

“This government will not give an inch when it comes to protecting our borders and will take every step necessary to ensure that people who have arrived illegally by boat are not rewarded with permanent visas,” he said.

The deputy prime minister, Warren Truss, said critics of the Coalition's asylum policy wanted it to fail.

Truss said he had encountered "widespread satisfaction" in the electorate with the fact that the policy was "working" to stop the arrival of asylum seeker boats.

He said the "constant critics" actually favoured an "open-door policy ... they don't want our policy to succeed," he told ABC's AM program.

Having quietly begun towing back boats towards Indonesia and with no asylum seeker boats arriving in Australia for the past three weeks, the prime minister, Tony Abbott, said last week he was pleased with the results of his policies although he was not yet “declaring victory”.

But the government has struggled to implement the policy to deny permanent protection to all asylum seekers who arrived before the former Rudd government began the policy of sending all boat arrivals to Nauru or Manus Island with no chance of settlement in Australia – a policy the Coalition government continued.

First Labor and the Greens combined in the Senate to overturn legislation reinstating Howard era temporary protection visas, which would have allowed those found to be refugees to work, but would require regular reassessment to see if protection was still necessary and would deny family reunion.

Morrison responded by freezing protection visas for the financial year at the number that had already been issued, as a backdoor way of achieving the same result.

Late last year, as the Refugee and Immigration Legal Centre, and barrister Richard Niall SC who successfully challenged the Gillard government’s 2011 Malaysian people swap policy in the high court, began a challenge against that freeze, Morrison revoked it.

He said he would now achieve the same goal though a regulation that came into effect on December 14, after parliament rose for the year, which prevented permanent protection visas for “all illegal maritime arrivals”.

But the case on behalf of the 15-year-old Ethiopian boy, who arrived in Queensland as a stowaway, and another on behalf of a Pakistani man who arrived at Christmas Island in May 2012 and is now in detention at the Yongah Hill centre in Western Australia, are also challenging whether that regulation can apply to asylum seekers who had previously made valid applications – estimated to be 4,000 or 5,000 of those in Australia.

The executive director of the Refugee and Immigration Legal Centre, David Manne, said the new regulation “fundamentally changed the circumstances in which a protection visa can be granted” and disqualified him when he was “on the verge of being granted protection, and was looking forward to getting on with rebuilding his life.”

All three high court challenges to the Morrison regulation are due for a directions hearing on January 23.

One grounds of appeal is that under the Legislative Instruments Act 2003 a government cannot reintroduce a regulation substantially the same as one that has been disallowed by the parliament within six months of the disallowance.