Ministers should be ready to give Thomas Cook "real financial support", a union representing staff at the struggling travel company has said.
The firm could fall into administration in days unless it finds £200m in extra funds needed to secure its future.
The Transport Salaried Staffs Association (TSSA) union has called on Business Secretary Andrea Leadsom to save Thomas Cook "no matter what".
Government sources suggest ministers are reluctant to bail out the company.
TSSA general secretary Manuel Cortes told Mrs Leadsom it was up to the government to save thousands of jobs and to allow Thomas Cook to "flourish".
He said in a letter: "It is incumbent upon the government to act if required and save this iconic cornerstone of the British High Street and the thousands of jobs that go with it.
"Thomas Cook can be a highly successful business and must be given every opportunity to flourish. I urge you to stand ready to assist Thomas Cook with real financial support."
Shadow business secretary Rebecca Long-Bailey said "all viable options" for saving the travel giant should be explored.
She added that "the government must consider stepping in and taking an equity stake to avoid this crisis".
BBC business editor Simon Jack reported on Saturday that government sources had questioned the financial wisdom of stepping in to save the company.
He said the government did not see its options as being between spending £200m to help Thomas Cook with its cash shortfall or £600m to repatriate its British customers abroad.
Currently there are 600,000 Thomas Cook customers on holiday, of which 150,000 to 160,000 are British.
Chloe Hardy from Leicestershire is due to get married in Zante in October and booked the wedding package with Thomas Cook back in June 2018.
Chloe and her fiance will also have 33 family members flying out, with their trips costing more than £33,000 in total.
With the big day looming, Chloe is frustrated by Thomas Cook's handling of their booking.
"I have emailed the wedding concierge and co-ordinator, neither has got back to me. We are unsure if we will be able to fly. Although, it's Atol-protected I have booked three weeks' leave from work and there's no guarantee that I will be able to get time off if I had to rebook."
"We've had constant questions from our family that we are unable to answer," she added. "This is causing great concern, worry and stress to all of us involved."
It comes after a noticeable shift in tone from Thomas Cook in its replies to concerned customers on social media.
Clients had earlier been told to ignore media speculation on Friday, but are now being reminded they have Atol protection - a sort of industry-backed insurance - "in the event that Thomas Cook goes into administration".
Thomas Cook, one of the world's largest travel companies, was founded in 1841 to operate temperance day trips, and now has annual sales of £9bn.
It employs 22,000 staff, 9,000 of those in the UK and serves 19 million customers a year in 16 different countries.
Thomas Cook's financial difficulties have mounted over the past year, culminating with the agreement in August of a rescue deal led by its biggest shareholder Fosun.
In July, Thomas Cook produced a business plan saying that it needed £900m in refinancing, up from a previous estimate of £150m. The £900m would come from Fosun, the group of creditors and some other investors.
The group of lenders then commissioned an independent investigation. Its financial advisers said Thomas Cook would require an additional £200m on top of the £900m already required, which would bring the total refinancing needed up to £1.1bn.
Thomas Cook succeeded in finding a backer to provide the additional £200m, but the BBC understands it has since pulled out and the group of creditors will not come back to the table unless that additional funding is found.
A final vote on that deal was due to take place this week, but it has been delayed until next Friday in the face of the latest demand for extra standby funding.
Thomas Cook has blamed a series of problems for its profit warnings, including political unrest in holiday destinations such as Turkey, last summer's prolonged heatwave and customers delaying booking holidays because of Brexit.
What are your rights?
If you are on a package holiday you are covered by the Air Travel Organiser's Licence scheme (Atol).
The scheme will pay for your accommodation abroad, although you may have to move to a different hotel or apartment.
Atol will also pay to have you brought home if the airline is no longer operating.
If you have holiday booked in the future you will also be refunded by the scheme.
If you have booked a flight-only deal you will need to apply to your travel insurance company or credit card and debit card provider to seek a refund.
When Monarch Airlines collapsed in 2017, the government organised to bring home all the stranded passengers, whether they were covered by Atol or not.
Are you a Thomas Cook customer or member of staff? If you've been affected by the issues raised here, you can get in touch by emailing email@example.com.
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