The union is returning fire on The Wilderness Society and lobby group GetUp!.
The activist groups placed an advertisement in Britain's Financial Times last month warning European banks they will be "pulping their profits" if they help finance Gunns' $2.2 billion mill.
The Construction, Mining and Energy, Union (CFMEU) on Thursday announced it had sounded a clarion call to global trade unions and confederations to push these financial institutions for proper due diligence on mill funding.
Union boss Michael O'Connor said they had capacity to influence European financial institutions and ensure they were not stampeded by a misleading campaign by Green groups in Australia.
"The people of Tasmania deserve this piece of nation building infrastructure," he said.
"We intend to push hard with our international affiliates to ensure the mill's funding is assessed on its merits."
The Wilderness Society's Paul Oosting said the union's campaign played right into their hands.
"The CFMEU's campaign will help to highlight the financial risks and massive community opposition to Gunns' proposed pulp mill," Oosting said.
However, voting in Tasmania's upper house election on the weekend undermined protesters' claims most Tasmanians oppose the Bell Bay pulp mill.
More than two-thirds of voters in the northern electorate, where the controversial mill is to be built, voted for pro-mill candidates in the election at the weekend.
A high-profile Greens, anti-pulp mill campaigner polled 16.23 per cent of the primary vote in Windermere.
Meanwhile, Gunns Ltd has government approvals to construct the $2.2 billion mill and is modelling marine effluent impacts for operational approval.
The company says it expects to sign a joint-venture partnership to help fund the $2.2 billion mill in June.
Source: AAP NewsWire