The UK government has said that the crisis at the Harland and Wolff shipyard in Belfast is "ultimately a commercial issue".
Unions say the yard is at imminent risk of closure and have called for it to be nationalised.
A government spokesperson said there was "every sympathy for the workers". They added that the government will "do all it can" to offer support.
It is understood administrators are now expected to arrive on Monday.
The firm's Norwegian parent company Dolphin Drilling is having serious financial problems and put Harland and Wolff up for sale late last year.
There were exclusive negotiations with a potential buyer but they cooled in the last two weeks.
On Monday, workers said they had taken control of the site and established a rota to ensure their protest continues around the clock.
The yard employs about 130 people, specialising in energy and marine engineering projects.
They said they would continue the protest until a solution is found.
More than 100 workers attended a rally in east Belfast on Tuesday in support of the shipyard workers.
On Tuesday, a UK government spokesperson said that the government has "every sympathy for the Harland and Wolff workers at a time of great personal uncertainty".
They added: "We will work with partners in Northern Ireland and in Westminster to understand the situation and do all we can to support, but it is ultimately a commercial issue.
"The Secretary of State for Northern Ireland, Julian Smith, has had conversations with Invest NI and ministers across government as a matter of urgency."
The Unite union said workers decided to take the action ahead of the expected arrival of administrators.
Trade unions have been hoping that the yard could benefit from plans to build more Royal Navy ships in the UK.
But now there is a risk it will not survive for long enough to benefit.
They have demanded Boris Johnson's government renationalise the yard and save their jobs.
BBC News NI Business Reporter Richard Morgan
Staff have been here since Monday afternoon, they took control of the shipyard in protest at its imminent collapse.
They remain here on Tuesday, they stayed throughout the night and they plan to do the same again tonight.
They want the government to intervene to renationalise the shipyard to prevent it from collapse.
More than 100 people attended a rally in support of the shipyard workers on Tuesday. Bombardier staff also attended.
Dr Esmond Birnie, senior economist at Ulster University, believes the government will be reluctant to renationalise the yard.
"The shipyard was nationalised in the 1970s, and remained in public ownership until 1989 when the Norwegian firm purchased it," he said.
"That was a period when a very substantial amount of public subsidy was put into it, so I think they will be reluctant, they will be cautious about going back down that route."
Harland and Wolff is one of Northern Ireland's best known businesses and its two huge cranes dominate the east Belfast skyline.
It was founded in 1861 and at the height of production during World War Two employed around 35,000 people.
Its best known vessel is the Titanic, which was built at the yard between 1909 and 1911.
'Here for the long haul'
Paul Beattie, who has worked for Harland and Wolff for more than 30 years, was on the picket line on Tuesday morning.
He told BBC Radio Ulster that workers "are here for the long haul".
He added: "We sat back for too long and left it in the hands of the politicians and management within the company and now we are two days from closure.
"So we have decided to take action and try to force our politicians into a position where they are no longer hiding behind the fact that Stormont is not running."
DUP MP Gavin Robinson told BBC News NI that he "understands and shares the concerns" and he is trying to work towards a solution.
He said: "The next number of days are critical for the shipyard and we are working towards a solution so I understand entirely their frustrations."
Mr Robinson added: "There have been talks with intended bidders- the people have a vision for this shipyard, the people want to see a renaissance in shipbuilding in Belfast."