The Green Party promised a $20 levy while New Zealand First said it would establish regional tourism funds to receive revenue from goods and services tax.
The TIA said international visitors generated in $14.5 billion in export receipts and paid $1.2b in GST.
''The government is enjoying a tax bonus from the tourism boom; it should reinvest part of the tourism dividend in infrastructure to support continued delivery of a quality tourism product.''
Davis said that in addition to the $75m infrastructure, training and conservation fund, the $1 billion Regional Development Fund was another ''possible'' source of funding for tourism.
The minister said there was no timetable yet for the implementation of the new border tax.
''We are working out the details including timelines in the months ahead.''
The last government angered the industry when it imposed a ''border clearance levy'' at short notice in 2015 and the TIA wants to be consulted on any new tax.
''Additional taxes are not favoured but any new funding models contemplated need to be fair, workable, efficient, applied nationally and ring-fenced for tourism related investments,'' the TIA briefing to the new minister said.
Travel agents have also raised concerns and want more details.
Chief executive of the Travel Agents Association of NZ, Andrew Olsen, said collecting the tax could be difficult.
''What we know is the airline ticket collection method will struggle to cope with residency as an exclusion. A large line of one million Australian visitors forking over $25 at the New Zealand gate will not enhance the airport experience or the easy clearance of the border and it could end in a reciprocity arrangement for New Zealanders entering Australia,'' he said.
Olsen said a user pays model should be considered.
''If the tourist visits a national park then they pay.''
It was common elsewhere and was not a direct tax on all travellers, including multiple entry business travellers who did not make such high use of public infrastructure.
The TIA also said user pays should be explored, and differential pricing for overseas visitors using national park huts.
It also said the recent introduction of the targeted rate by the Auckland Council on accommodation was poorly designed and unfair.
''A range of regional taxes would be confusing to visitors and a badly designed tax system would harm New Zealand's brand and attractiveness as a destination.''
But Davis backed local authorities to make their own decisions.''Local councils are independent of central government and need to make their own decisions in the interests of their communities. This includes supporting the development of facilities used by both residents and visitors,'' the minister said.
The TIA also said immigration changes could badly affect operators' ability to find suitable staff.
About 188,000 people were employed in tourism and the industry would ''be very concerned'' if proposed changes to temporary work visa settings cut the supply of workers at a time when the industry was growing.
