They were invited to meet the First Minister as efforts continued to find a way of saving the 1700 jobs at the plant which bosses say is losing £79,000 a day.
Lawrence Wason, divisional officer with Usdaw, which has around 800 members at the plant, said Mr Salmond had been “very constructive” during the 80-minute meeting at his official residence.
Mr Wason said: “He is very concerned about the situation and from his point of view he is on the same page as the trade unions. He wants to make sure no stone is left unturned and we get a grip of the whole situation and what, if anything, can be done.”
Parent company Vion announced earlier this month that it planned to close the factory, which produces products including sausages, haggis and black puddings.
The Scottish Government has established a task force, bringing together the company, unions, West Lothian Council and others in a bid to save the plant.
The unions are still studying information about the factory’s performance in an attempt to understand how it went from a planned £20 million expansion and the promise of 250 new jobs last September to such heavy losses that the company said it had to close.
Mr Wason said: “The announcement on July 5 came as a major shock to everyone concerned. It was the last thing people were expecting.”
He said it was early days for any solution to be in the offing.
But he said: “We are trying to think positive. We don’t want to give anyone false hope, but we need to make sure everything is fully explored.
“The company is maintaining one of the biggest problems is the footprint and layout of the plant. They are saying some of their competitors have the whole process in one straight line, whereas the Broxburn site is a bit mixed and matched, with bits added on. It has grown and evolved.”
He said the company also cited rising utility costs, the price of animal feed and diesel, as well as over-capacity and fierce competition in the UK meat processing market.
A spokesman for Mr Salmond said: “The First Minister met with Usdaw representatives to discuss the work of the Hall’s of Broxburn task force so far. The First Minister emphasised the Scottish Government’s concern and assured them of our support. The next meeting of the task force is on July 30.”
A spokesman for Vion said consultations with staff and unions were continuing.
He added: “There had been briefings with staff and unions during the course of the year to outline the major challenges which the plant was facing and make clear the seriousness of the situation.
“The complex nature of the site and its inefficient layout have been key factors in the decision, despite the heavy financial investment which has been made.”