"But it must be done with the least possible inconvenience to New Zealand consumers," he said.
A discussion paper showed the Government was forgoing $180 million in revenue because online shoppers were not paying tax on services and goods bought overseas.
Of this total, $40 million was related to online services, like digital downloads.
To capture this lost revenue, officials proposed getting overseas companies to register for GST if their turnover in New Zealand exceeded a certain threshold.
Big foreign companies like Apple and Amazon were expected to sign up, but the final decision on the turnover threshold could influence whether smaller companies continued selling to New Zealanders.
New Zealand Initiative economist Eric Crampton said: "Some of the bigger outfits might be concerned about having too high a threshold because then they would face smaller competitors who aren't subject to that GST requirement.
"But if you do set it low enough then those [smaller competitors] are just going to stop selling to New Zealand entirely." New Zealand-based companies whose turnover exceeded $60,000 had to register for GST.
The threshold for overseas companies could be set as low as $10,000.
The Government was asking for submissions on this threshold.
Once companies had registered, the GST would then be collected at the point of sale. If New Zealand consumers somehow managed to avoid paying GST, they could face stiff penalties of up to $50,000.
Dr Crampton said this rule could potentially capture people who used virtual private networks (VPNs) to stream overseas television, such as the US version of Netflix.
As for the issue of applying GST to lower-value imported goods, the Government said this was more complicated and would take longer to work out.
Retailers NZ, which has been lobbying hard for the change, said it was disappointing that New Zealand-based shops would continue to operate at a disadvantage to overseas businesses.
Q & A:
Will I have to pay more for online purchases?
Probably. The Government wants consumers who buy online services from overseas suppliers to pay GST. Any increase in prices will depend on how much these firms pass on in costs.
Will this affect things I buy online in New Zealand?
No. GST is already collected on these products.
When will the rules change?
GST is likely to be introduced next year for online purchases from foreign websites.
What sort of things will it cover?
Nearly any service or intangible product bought on the internet from overseas. This includes downloads or streaming from Netflix and iTunes, but also more traditional services, including legal or accounting advice.
What about physical goods I've bought from overseas?
This issue will be dealt with later by the Government. But it has signalled that goods bought online worth as little as $20 could include GST, down from the current threshold of $225-$400.