The company has been working on a plan which it said "will provide the basis for the agreement of a proposal to restore Carillion's balance sheet".
One of many private companies to run public services in Britain, Carillion is fighting to survive after costly contract delays and a downturn in new business prompted a string of profit warnings and a first-half loss of more than 1 billion pounds ($1.4 billion).
The troubled contractor said it "continues to engage in constructive discussions with a range of financial and other stakeholders regarding options". It was also behind key construction projects including London's Royal Opera House, the Tate Modern gallery and the Channel Tunnel rail link.
Earlier this week, Carillion presented a revised business plan to scores of lenders - but contrary to reports, this was not expected to produce an instant agreement with them.
The share price fall will come as no surprise to City analysts, many of whom have already written off the equity value of the contractor, which employs nearly 50,000 people worldwide.
But it is perhaps best known for being one the largest suppliers of services to the public sector.
The company is a major supplier to the Government, maintaining prisons across the country and managing around 900 schools.
A Government spokeswoman said: "Carillion is a major supplier to the Government, with a number of long-term contracts".
In a note to clients, Peel Hunt's analysts said: "We suspect that given its mounting liabilities, recent press comment, growing customer worries and supply chain hesitancy that Carillion will be forced (by the banks) to accelerate its financial restructuring".
He added that workers "should have protection and guarantees from the government, including an assurance that operations will be directly transferred over to Network Rail with all jobs, pensions and rights safeguarded if Carillion goes bust".
The company held talks with its lenders and advisers in London on Wednesday.
The rescue plan shown to lenders on Wednesday includes handing back some loss-making contracts, revising the terms of others and potentially accepting financial support from the Government if it can not secure it from private sector sources.
Tensions around the 200-year-old company have been ratcheting up for weeks and on Thursday ministers overseeing everything from justice to transport, health and education met to discuss how they should respond to the possible demise of a business that plays a central role in British public life.
The Government is being urged to bring contracts from construction giant Carillion back into public control amid fears it could "collapse".
A Government spokesperson repeated a statement given to Sky News last weekend which said it was "committed to maintaining a healthy supplier market and work closely with our key suppliers".
A spokeswoman for the Pension Protection Fund said it was "aware of the discussions between the company, government and banks and, along with the trustees and the Pensions Regulator, will act as it always does to protect the interests of Carillion scheme members and levy payers".
A Downing Street spokesman also said the Government was monitoring the unfolding situation. "We will not comment further unless it becomes appropriate to do so".
Last week, the company was dealt a fresh blow when the City watchdog launched a probe into the "timeliness and content" of statements it made to the stock market about is financial position between December 2016 and July a year ago, when a massive profit warning sent its shares crashing by 75%.