More than 250 men working for contractors on the LNG site at South Hook, Milford Haven, have walked out over safety issues.
The men - mainly welders, steel erectors and labourers - are concerned over the removal of asbestos from the site.
They downed tools last week and refused to go back on Monday.
Following a meeting, union steward Douglas Corbett said that there had been a totally negative response' from management of contractors CB&I (Chicago Bridge and Iron).
A spokesman for the company said small quantities of asbestos cement pipe had been found last year in the concrete foundations of the old Esso refinery site where the LNG terminal is being built.
But Mr Corbett said: "We know that lorries, have been leaving the site in the early hours of the morning with material contaminated by asbestos."
"We have had a meeting with management and told them the site is unsafe." He said the men wanted safety assurances but these had not been given.
But he added: "There is no such thing as a safe level of asbestos.
The safest thing is for the men to be off-site while the contaminated material is removed.
"We will be meeting at the same time next Monday to discuss any developments. Hopefully the management will come to their senses. They have badly mishandled this and have acted in a very cavalier attitude, totally disregarding the safety of the men, their families and the local community."
A spokesman for South Hook said that there was nothing secret or clandestine about the operations.
The company had been working for months with the Environment Agency and Health and Safety Executive over the methodology and handling of the contaminated waste and this had been approved, he said.
The reason the lorries left the site in the early hours of the morning was for logistical reasons as the waste was being taken to designated sites in Middlesborough.
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