He said there should be no restrictions on the industry once supply in New Zealand was met.
He said five financial quarters of recession was forecast and Government intervention would be needed.
Without support, "we're going to see a wave of closures or shifts", he said, and a push to buy local logs for local projects Could ease the uncertainty.
Verry said the industry was working with the Ministry of Business, Innovation, and Employment and Housing New Zealand to ensure projects already under way, and those about to get under way, did.
Jones said the needs and appetite of downstream processors needed to be satisfied before international buyers.
The minister would put forward a proposal of a levy on exported logs and a register of log-buyers.
The sector generated $6.8 billion revenue, 55 per cent of which was from international trade with China as a primary trading partner.
He said the forestry sector needed to expand in New Zealand creating a better range of products.
Jones said a reference group which was made up of ministers David Parker, Damien O'Connor, Eugenie Sage and James Shaw, had discussed options to incentivise trade of downstream processing to guarantee the delivery of adequate raw material to the local processing sector.
"I want to be absolutely explicit, the Government has no agenda to ban exports."
He said the Government wanted forest owners to prioritise New Zealand needs and the downstream processing industry over selling raw logs internationally.
"A lot of owners of the forest believe it's not their job to solve the unemployment woes or manufacturing management woes," and prioritised maximising profit for their owners who were predominantly foreigners, he said.
The Forest Owners' Association had told him about a predicted spike in international prices due to shortages overseas and were keen to take advantage of this.
On Tuesday, parts of the forestry sector could begin working again while others which supplied essential wood continued throughout lockdown.
Uptake of the Government's wage subsidy had been high among the sector, Jones said.
Nearly 90 per cent of respondents in a Te Uru Rākau forestry sector survey done on March 31 reported having either applied or were receiving the subsidy.
He welcomed the start-up next week.
Further announcements to support the forestry sector and its large workforce will be made in the next few weeks, Jones said.
Forestry sector businesses that can operate at alert level 3:
• Forestry management including aerial spraying, weed and pest management.
• Nursery operations, planting and seed collection.
• Log harvesting and haulage.
• Log sales.
• Wood processing.
