Sunway says it is also suspending all subsequent weekly flights to the holiday destination due to the continued uncertainty in the region since the terror attack that killed 38 tourists last Friday.
The late decision was announced as final preparations were made for the return of the remains of the three Irish people who died.
Funeral arrangements for Larry and Martina Hayes, the married couple from Athlone, Co Westmeath, were confirmed yesterday.
Their removal will take place this evening to the Church of Saints Peter and Paul in Athlone and they will be buried together in Coosan Cemetery after funeral Mass at 11am tomorrow.
It is expected to be one of the biggest funerals the town has ever seen. Bus Éireann inspector Larry, known to many as Lonnie, and Martina, his wife of 32 years, were well known and popular. Martina was from the large Kelly family. She was one of 11 siblings.
Details of the funeral arrangements for Lorna Carty from Robinstown, Co Meath, whose husband Declan survived the attack, were still being finalised last night.
As their families prepare to receive the victims, the impact of the attack is continuing to spread. Sunway Travel had said it would go ahead with its weekly departure tomorrow once customers still wanted to go and as long as the Department of Foreign Affairs held off issuing a no-travel advisory.
However, the company yesterday changed tack and said it would not fly to Tunisia again until it had a clearer picture of the security situation on the ground.
“Due to the current uncertain situation in Tunisia, Sunway have decided to suspend the weekly flight schedule to Monastir from this Friday 3rd July until the situation is clarified,” it said.
“Our return flight on Friday July 3 from Monastir to Dublin will go ahead as scheduled. We have not taken this decision lightly but believe it to be in the best interests of our customers.”
The company acknowledged that the last-minute change of plans would disappoint some customers but said it would accommodate them with a full refund or a holiday in an alternative Sunway destination.
While Sunway charters the flights, several dozen seats are used by travel operator Just Sunshine, which now also has to tell customers they cannot fly.
Spokesman John Grehan said customers who had already requested to change their plans prior to the cancellation announcement had been offered alternative Sunway destinations or refunds.
Those affected by the cancellation will receive a full refund but will have to make their own alternative plans.
Any passengers booked on today's flight to Tunisia are being offered a full refund should they choose not to travel.— Sunway Holidays (@Sunway_Holidays) June 26, 2015
The decision to suspend flights was taken despite moves by the Tunisian authorities to increase the presence of police and army in tourist resorts yesterday.
Irish holidaymakers who had arrived just hours after the attacks have said in recent days that there had been no visible security outside their hotels.