It is similar to legislation implemented by the former National government in 2014, opposed then by Labour and the Greens, after Cyclone Ita flattened large swathes of native forest in the region.
"This is a practical Bill which embraces environmental responsibility and supports regional economic development," Pugh said today.
"Removing and processing these trees which would otherwise lie decomposing on the West Coast forest floor would provide jobs for the region along with clearing space for native regeneration – two areas which NZ First claims to be passionate about," she said.
Jones said he would be pushing for support for the Bill.
"It would be foolish of me not to reflect the fact that people from the West Coast, they're really keen that wood remains accessible. I know it's on the DOC estate.
"I guess it's me against the huhu in terms of the eco-system but jobs are really important."
He acknowledged there were diverging views between NZ First and the Greens but "you should expect this in MMP politics".
"The timber is dead and we are planting millions of new native trees. It seems a perfectly legitimate way of recycling natural resources to give jobs to parched regions.
"I am more interested in woodwork than woodworms for Coasters."
Two Labour MPs, Damien O'Connor and Rino Tirikatene, voted with National on the 2014 bill.
Today O'Connor, speaking as the local MP, said he had always supported utilisation of sustainably harvested timber.
"I'd need to see the detail of the Bill to ensure it's not just a grab for any timber that happens to fall over and it would be important that all parties work together to ensure any harvesting of windblown timber was done responsibly."
Comment is being sought from Conservation Minister and Green MP Eugenie Sage.
West Coast Regional Council chairman Andrew Robb said the Ita legislation sparked a revival in the indigenous timber processing industry, creating jobs in forestry, sawmilling and transport.
"If we are successful with this local bill, we can ensure that we can keep these jobs and keep this sector of the economy going."
Work done under the Ita legislation had shown windblown timber could be safely recovered without significant harm to the conservation value of harvest areas. It had also provided significant revenue for the Department of Conservation to protect conservation land from plant and animal pests, Robb said.
A review of the Ita legislation was highlighted as an initiative in the West Coast Economic Development Action Plan released in July 2017.
Around 20,000ha of forest was felled by Cyclone Ita in 2014 and the law change allowed beech, rimu, totara and matai trees to be harvested on the conservation estate on the condition that they were taken outside classified areas and used for finished products and not firewood or wood chips.
"Since Cyclone Ita the West Coast has experienced other severe weather events which have resulted in further windblown timber opportunities," Robb said.
"Under the current legislation these have not been able to be realised."
The council will consult on the proposed bill before a decision is made on whether to adopt it. Pugh would then sponsor it and introduce it to Parliament.
