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The assembly passed the first step in devolving air passenger duty (APD), on 28 May 2012.
The UK Finance Bill 2012 was introduced in the Westminster Parliament on 10 May 2012.
It included the provision to devolve direct long-haul rates of APD to Northern Ireland.
The assembly's approval to a legislative consent motion means the Westminster Parliament would be given consent to proceed with the bill.
Finance Minister Sammy Wilson explained that if the relevant powers were devolved, the assembly would have the power to set its own rate of tax.
He explained that the programme for government showed that the executive would like to set the rate for direct long-haul flights to zero.
Finance committee chairman, Sinn Fein's Conor Murphy described APD as "a regressive tax" which was a "disproportional burden" to Northern Ireland due to the region's greater dependence on air travel.
He said the committee had given general support to reduce the tax on direct long-haul flight but said it wanted fuller devolution of powers to cover short-haul flights
"The committee concluded that it had been presented with a strong case for reducing or abolishing APD rates on the 98.5% of flights from the north which fall into the domestic/short-haul Band A as a measure to improve the nation's connectivity to Britain and other EU states," he said.
The finance minister said there were no proposals in place to provide a reduction or removal of the tax on short-haul and domestic flights.
"The policy framework to provide for this is simply not in place," Mr Wilson said.
"The executive has not agreed such an approach, nor at any time have these powers been requested from the government by the executive."
The minister said devolving and setting a zero rate of tax for direct long-haul flights would cost the executive £5m per year.
He said this would rise to at least £60m annually if short-haul flights also had this rate.
"While agreeing the policy on short-haul APD rates may be relatively straightforward, gaining consent to the financial implications would not," he added.