Carillion was in talks with the government since October as part of a desperate bid to stave off collapse, according to the chief executive.
Keith Cochrane says the construction giant was left with just £29m in cash by the time it went bust on Monday.
Until the last moments, directors still believed a rescue was possible, but banks became more demanding, he said.
The details are included in a document Mr Cochrane has prepared as part of the insolvency process.
His statement sets out attempts to save Britain's second-biggest construction company after three profits warnings and a collapse in the share price.
Efforts to sell off parts of the business failed and Carillion's banks became more demanding, only agreeing fresh funding under tight new conditions that the company was unable to meet, the statement discloses.
There had been regular meetings with the government and its advisers in the final few months of 2017, Mr Cochrane says. But on 31 December a "formal request" was made for support from the government.
Even as late as last weekend, directors believed that "a constructive dialogue" was underway with banks and the government about providing short-term funding.
Directors wanted the government to "guarantee" more funding for four months while Carillion continued its restructuring, and be allowed to defer tax payments. Both requests were refused, according to Mr Cochrane.
But his document adds that "certain of the group's lenders took unilateral action which in the company's view undermined the group's efforts to conserve cash".
He singles out Royal Bank of Scotland (RBS) as one of the banks that wanted to impose tough new lending conditions.
RBS said in a statement to the BBC that it had "provided considerable support and forbearance to Carillion over many months".
"The judgement of the bank was that the restructuring plan put forward by the company was not viable and therefore we took the difficult decision not to extend further funding and increase our exposure to the business."
Running out of cash and owing more than £1.3bn to its banks, Carillion declared itself insolvent on Monday.
Rather than attempt an orderly administration of Carillion in the hope of salvaging something from the business, the Official Receiver was appointed to liquidate the business.
Accountants EY and PwC both rejected requests to become administrators because there was no money left to keep the company ticking over, Mr Cochrane says.
Meanwhile, Treasury minister Liz Truss told the Commons on Tuesday that "it would be completely wrong for a public company that got itself in this state to be bailed out by the state".
Business Secretary Greg Clark has asked for an investigation by the Official Receiver to be broadened and fast-tracked.
The conduct of directors in charge at the time of the company's failure and previous directors will be examined.
"It is important we quickly get the full picture of the events which caused Carillion to enter liquidation," said Mr Clark. "Any evidence of misconduct will be taken very seriously."
At the same time, the role of Carillion's auditor, KPMG, will be examined by the Financial Reporting Council.
The company employed 43,000 people worldwide, 20,000 in the UK, and had 450 contracts with the UK government.
The government has said that staff and contractors working on public sector service contracts will continue to be paid. But there is concern that big projects, including the construction of hospitals and roads, will be delayed while the details are worked out.
There are also big worries for an estimated 30,000 smaller firms which have been working on Carillion projects in the private sector.
Many are owed money and are waiting to find out if they will get any of it back.
'I had to make 10 people redundant yesterday'
Andy Bradley is the managing director of Flora-tec, which is owed £800,000 by Carillion for landscaping services.
"The government actively encouraged businesses like mine... to get involved in public sector contracts, to make sure the little guy got a slice of the pie.
"When Carillion started to get into trouble last year we were considering that we would scale back our involvement with them.
"However... the government continued to give them billion-pound contract after billion-pound contract and that said to me, as a small supplier, that the government had done their due diligence.
"We were following the government lead... only to be given a sucker punch.
"I had to make 10 people redundant yesterday. That's 10 people with mortgages, car loans, all that stuff. It's an absolute disgrace."
On Monday, the government said that firms working on Carillion's private contracts would be paid for another 48 hours. But the latest statement from the Insolvency Service indicates there might be more flexibility.
It says that the liquidator is talking to Carillion's private sector clients about which services will continue; however contracts will be ended if the client no longer wants to pay for them.
"No one has been dismissed at this point and staff will continue to be paid for the work they perform," a spokesperson for the Insolvency Service said.
Carillion was hit by cost overruns on big projects, problems with contracts in the Middle East and a large deficit in the company pension scheme.
Chief executive Richard Howson stepped down in July last year after a profit warning. There has been much criticism over the size of Mr Howson's pay award in 2016 which, including bonuses, totalled about £1.5m.
Finance director Richard Adam, who retired in December 2016 after nine years at Carillion, received almost £1.1m in salary and bonuses in 2016.
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