Highland Airways has carried 37,000 people between Cardiff and Anglesey in the last two years
Calls for clarity on the future of the north to south Wales air route are made after the air firm running it said it was facing "continuing problems".
The twice-daily route between Anglesey and Cardiff is operated by Highland Airways with £800,000 public subsidy from the Welsh Assembly Government.
Tenders for a new contract for the route ended on Wednesday and it is understood only Highland Airways bid.
Deputy First Minister Ieuan Wyn Jones described it as an "essential link".
""This service provides an essential link between North and South Wales and has been a huge success with passenger numbers far exceeding expectations," he said.
""Since it begun in May 2007, it has attracted 37,000 passengers."
Mr Jones added the Welsh Assembly Government remained committed to maintaining the service.
"We have had contact throughout the day with Highlands Airways and will continue to do so that they keep us up to date with news on potential investors.
"Our main priority is keeping this service going.
"Ideally, we want Highland to remain running this route whilst they look for new investors.
"If this is not possible and we face a worse case scenario with Highlands going into administration, we hope any administrators could continue the service.
"If the administrators were unable to do this, the assembly government will look for an interim solution to continue running the route - we feel we could do this fairly quickly to ensure passengers continue to have a service. One option would be to issue an interim contract.
"We are also in the middle of a re-tendering the service as our current contract with Highland Airways expires in May."
Highland Airways was awarded a three-year contract to run the north-south Wales route from May 2007.
But it is currently not taking bookings for any flights.
The deadline for airlines to tender for the new contract, starting in May this year, closed last Wednesday.
It is understood that the only bidders are Highland Airways, but the Welsh Assembly Government has not confirmed this.
The route has a Public Service Obligation (PSO) condition on it, which means there are fixed standards of continuity, regularity, capacity and pricing.
The PSO, the first of its type in Wales, specifies a range of service-related requirements, such as frequency and timings, aircraft capacity and fare levels.
Liberal Democrat transport spokesperson, Jenny Randerson, said she had concerns over the matter.
"It is particularly worrying that only one bid was received by WAG (Welsh Assembly Government)," she said.
"This does suggest that despite huge public subsidy, this service is still not seen as a viable, profitable, and green solution to this key transport need."
Ms Randerson said the Labour-Plaid assembly government must seek full assurance of the financial stability of the "private entity receiving this large public subsidy".
She added that the Liberal Democrats were opposed to such a large subsidy being given to a service which so few Welsh citizens were able to access.
An Isle of Anglesey County Council spokesperson said: "Any issues involving the operation of the contract would in the first instance be a matter between the assembly and the airline."
Management at the Inverness-based airline met with staff on Monday morning, and told them they were still hopeful of survival - despite what was described as "continuing difficulties".
Commercial director Basil O'Fee said in a statement: "The company is currently facing difficult trading, most recently exacerbated by the severe winter and resultant reduced flying and reduced income.
"The board has been seeking new investment and has been in discussion with several parties in recent weeks.
"The outcome of all these discussions should be judged within days rather than weeks," he said.
"In the meantime the company continues to trade normally, fully supported by all our staff and continues to enjoy the support and encouragement of its many stakeholders and customers," he added.
The airline operates flights from Inverness to the Western and Northern Isles, as well as in Wales.
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