The decision will be delayed because of the cost to the block grant for funding public services amid the economic squeeze, Arlene Foster added.
The Executive is scrapping the duty on long-haul flights such as the Continental service from Belfast to Newark and bearing the cost of that change itself.
However, many more short-haul flights would be affected by a decision to abolish it altogether and the cost could be millions of pounds, a committee of MPs heard.
Ms Foster said: "At present our plans are not to reduce air passenger duty for regional flights because of the cost to the block grant at a time when we are being squeezed. In relation to wider issues however, it is something that will remain on the agenda, it is not a dead issue."
A European legal ruling aimed at preventing unfair bias in favour of certain regions means if the Northern Ireland Executive wants a lower rate of duty than the rest of the UK, it will have to fund it from spending on public services allocated by Westminster.
Ms Foster and regional development minister Danny Kennedy were briefing the Northern Ireland Affairs Committee at Westminster.
On Monday the chief executive of BA owner IAG called for the duty to be scrapped across the UK. Willie Walsh said the levy is damaging the economy.
Air passenger duty across the UK rose by 8% this spring. For short-haul flights, the tax has increased from £12 to £13. For long-haul flights of more than 4,000 miles, it has gone up from £85 to £92.
BA warned last year it would hire 400 fewer people because of the rise, adding the harm to the economy exceeded the revenue raised. The Treasury has said the aviation sector had to play its part in restoring the public finances.