Mr Dutton is seeking special leave to appeal this decision.
National Justice Project principal solicitor George Newhouse, who along with law firm Maurice Blackburn acts for the asylum seekers in the four cases, said he would fight Mr Dutton’s application for special leave to appeal.
“The application is simply designed to frustrate the ability of very sick people to seek healthcare by making an application to the Federal Court,” Mr Newhouse said.
It will also determine whether the substantive compensation claims will go ahead in the Federal Court, seeking damages over the alleged delaying of asylum seekers’ medical treatment.
A Senate hearing last month heard that asylum seekers were waiting an average three years to be transferred for medical treatment.
If Mr Dutton is successful, it will mean the High Court itself will be the only jurisdiction that can hear the cases.
The High Court is a more expensive and challenging jurisdiction in which to lodge a claim.
A Home Affairs spokesman confirmed the government had applied to the High Court for special leave to appeal the Federal Court’s decision in four test cases related to “the correct jurisdiction in which medical transfer proceedings should be commenced”.