Flybe boss Mark Anderson has told staff that he and the management team remain "focused" on turning the airline round.
Mr Anderson's comments came in an email to staff following reports that the airline is in crisis talks in an attempt to put together a rescue deal.
According to Sky News, Flybe, which has already been bailed out once, has been struggling to secure fresh finance.
In his email, Mr Anderson stressed that Flybe was continuing to operate as normal.
"All my energy, and that of our Leadership Team, is very focused on continuing to turn Flybe, soon to be Virgin Connect, around and deliver the heartfelt service that our customers expect," he said.
"I do appreciate that the headlines some of you have already read are disturbing but I want you to know that we are determined to do everything we can to make this work."
He told staff he was "extremely grateful" for their hard work and commitment.
In an earlier statement, Flybe said it was focusing on "providing great service and connectivity for our customers, to ensure that they can continue to travel as planned".
Flybe, the UK's biggest regional carrier, added: "We don't comment on rumour or speculation."
The reports come a year after Flybe was bought for £2.8m by a consortium including Virgin Atlantic and Stobart Group.
Since then, the consortium has invested tens of millions of pounds in the troubled carrier, but losses have continued to mount.
Tourism adviser and researcher Prof Annette Pritchard, of the Welsh Centre for Tourism Research in Cardiff, commented on Twitter that Flybe provided "a vital social and cultural link for many marginal economies".
Based in Exeter, Flybe carries about eight million passengers a year from airports such as Southampton, Cardiff and Aberdeen, to the UK and Europe.
Its network of routes includes more than half of UK domestic flights outside London.
If the business collapses, more than 2,000 jobs will be at risk.
Matthew Mills, a graphic designer based in Shropshire, recently booked flights for his family to Germany with Flybe.
He is also one of the 10,000 consumers still waiting to receive a refund from collapsed travel firm Thomas Cook on a holiday that was meant to take place in November.
"You don't know whether to laugh or cry," he told the BBC. "We've used Flybe quite a bit in the past because we have family in Germany and we don't have many alternatives in the UK - if Flybe goes under, we'd be looking at 50% more in prices on flights to Germany, easily."
Worried Flybe customers have taken to Twitter to express their concerns, saying they are still waiting for information on whether their flights will go ahead.
Please don't collapse #Flybe I need you for those awkward flights to locations people don't want to go to. Your business model works perfectly for me, maybe not the rest of the world but its great for me!— Tadeusz Borowski (@TadeuszBorowski) January 13, 2020
#Flybe nooooo how do we get to the Channel Islands and see family. Just booked Easter flights.— Carol Scott (@Motherinlaw01) January 13, 2020
The BBC understands that EY has been lined up as administrators if Flybe were to go under.
Brian Strutton, general secretary of pilots' union Balpa, said: "I am appalled that once again the future of a major UK airline and hundreds of jobs is being discussed in secret with no input from employees or their representatives.
"According to reports, the airline could have collapsed over the weekend, which would have been devastating news."
Mr Strutton called on Flybe's owners and the government to talk to the union, saying staff had a right to know what was going on.
Exeter is home to Flybe's headquarters and a quick look at the departures and arrivals board here illustrate just how important the airline's connections are to the area. Of the eight departures to destinations such as Manchester, Newcastle and Jersey, seven of them are operated by Flybe.
The taxi driver who brought me from the train station told me his firm had paid £40,000 to secure a concession inside the terminal. "Flybe is a massive part of our business" before helpfully reeling off a list of arrivals and departure times he knew off the top of his head. Its not just the flights - over 400 people work at HQ, plus they run a training academy for apprentice plane engineers.
The airline is in talks with both the Department for Transport and the Business Department to see if the government can provide or facilitate a rescue. The government refused a request from Thomas Cook for £150m in emergency funding, with Boris Johnson claiming it would have provided a "moral hazard" - a dangerous precedent that would see the government called on to rescue other failing private companies.
However, the government may face a political hazard. It has vowed to focus on regional connectivity which the collapse of Flybe would do nothing to improve.
Prof Loizos Heracleous, an aviation industry expert from Warwick Business School, said it would be "no easy task" for Flybe to attract new finance.
He added: "The aviation industry is an unattractive industry in terms of performance and returns on investment at the best of times.
"It is saddled with high-cost assets, namely planes, and key costs that fluctuate uncontrollably, mainly fuel, which accounts for around a third of total airline costs.
"On top of that, they face high regulation, often aggressive unions, low barriers to entry that increase competition, and high bargaining power of buyers."
Ben Bradshaw, Labour MP for Exeter, said Flybe provided "valuable connectivity throughout the UK" and called on the government to intervene. He called Flybe "a strategically important business".
The industry regulator, the Civil Aviation Authority, said: "We do not comment on the financial situation of any of the organisations we regulate."
As long as Flybe carries on flying, there is no need to worry and certainly no reason to try to get your money back, writes Simon Gompertz, BBC personal finance correspondent.
If the airline was to fail, however, all flights would most likely be cancelled. Those with paid-for bookings could find they lose their flights and their cash.
If your flight is part of a package deal covered by the ATOL scheme, then you should be protected and have the right to a re-booking or refund.
Otherwise you can try to retrieve the money from your credit card company, if that's how you paid. There is also a debit card chargeback scheme which can help.
Many travel insurance policies are not much use in these situations, unless you stumped up extra for the Scheduled Airline Failure option or something similar.
Those stuck overseas might be left hoping that the government will direct the CAA to step in, as it did when Monarch and Thomas Cook went under, to bring back stranded passengers for free.