Chief executive Steve Heapy said the company is seeing aircraft "emptying" on routes to the eastern Mediterranean, although demand for western Mediterranean destinations remains strong.
Heapy had been due to attend the annual Jet2 conference in Cadiz, Spain, but said he was unable to travel after remaining in London for meetings with officials, including those from the Department for Transport and the UK Civil Aviation Authority, to discuss the operational impact of the conflict.
Speaking via a recorded message to 350 agents, Heapy said: "Bookings to Cyprus and Turkey are drying up, cancellations are up and our aircraft are emptying."
However, he said the company was working to cross-sell customers to western Mediterranean destinations where demand "seems to be okay".
Heapy added that Cyprus remained a safe destination despite being among the most affected by the drop in demand.
He said: "Cyprus is still far enough away that you can still travel. We’re doing what we can to understand what’s going on and how we can work our way through it."
'We're a very resilient industry'
Heapy also predicted a swift recovery in demand once the situation stabilises, saying: "I think we should all be prepared for hopefully a pretty swift end to the conflict and a pretty sharp bounce back when that happens."
He predicted hoteliers in Cyprus and Turkey would introduce special offers in the coming weeks as they seek to maintain occupancy levels, while adding that Jet2holidays was also speaking with hotel partners in the western Mediterranean to ensure they don't "get greedy" and instead keep prices competitive.
Travel agents were also told to remain positive as Heapy emphasised the resilience of the sector.
"We'll do what we can to work with you and fight to get through this the best we can," he said. "Our job is to put our customers’ fears to one side and reassure them that these destinations are safe.
"We’re a very resilient industry. These events happen every couple of years, and I'll do whatever I can to help all our of businesses navigate through this."