The current rate in the Republic is already much lower than the equivalent air passenger duty in Northern Ireland - €3 compared with £13.
According to the DUP's Mr Hamilton, the discrepancy is already unfair.
"We have made it clear to the UK Government that we regard APD as an unfair tax that disproportionately affects regions in the UK - and Northern Ireland in particular, where alternative transport options are more limited and where the option of travelling from Dublin exists," he said.
"PWC, on behalf of the major airlines, provided evidence to the Chancellor in the run up to Budget 2013 of the benefits that the abolition of this duty would bring to the whole of UK, including Northern Ireland, if it were removed."
NI air travel tax position 'unchanged' - UTV Live News