Up to 180 drivers did not report for work with Arriva last week, the company said in its latest update.
More than half of them, it said, were from the old regime.
Arriva Malta managing director Keith Bastow thanked the drivers who worked hard and went well beyond their call of duty over the past week and promised that Arriva was adamant to fix the problem.
"We started operating services a week ago with the huge challenge of being without a considerable number of the drivers who were due to help us provide public transport services.
"That a significant number of people who signed contracts didn't honour their commitments hit us hard...
"We were then, and are now, far from where we would want to be, and from where the client body, Transport Malta, and our customers would want us to be."
However, he said Arriva was determined to deliver the public transport system that the people of Malta deserved and "we will not give up or lose heart at this bad start."
Services, he said, had again improved today with more frequent travel opportunities for passengers. However, there were localised issues which still needed fixing.
"We have continued to put significant resource and effort into transporting passengers around the island, and are now concentrating on building the consistent regular, sustainable service that passengers need to be able to depend on.
"To help us do this, we have drafted support from around the Arriva group to bring in additional specific transport expertise and to take the pressure off staff who have this week worked around the clock, above and beyond the call of duty.
"More than 40 support staff, supervisors and management are supporting our team," he said.
Mr Bastow said that more than 70 temporary drivers from the UK had now been drafted and a recruitment drive in Malta was continuing.
By tomorrow, more than 50 British drivers will be on the road, with a further 20 entering service early next week.
These drivers were trained on the specific routes they will be working on.
"We have also continued to recruit and train additional drivers in Malta, which we would have been doing anyway to provide holiday cover for later in the year.
"We currently have 54 Maltese drivers in training and are actively recruiting more."
Mr Bastow said that to address issues with services in more remote areas with lower passenger numbers, the company was temporarily sub-contracting some of the routes with the consent of Transport Malta. Vehicles on these routes would clearly display an Arriva logo and route number.
"From management down to drivers, we are taking action, and are determined to fix this.
"Apologies to those who have been affected this week – we are putting as much resource, expertise and effort as we can into making sure that a better service is provided for you next week.
"Thank you to the public for their feedback and for their support.
"We will work with you to give you the better bus services that would back-up the good customer service you are telling us you have had from our drivers.
"To the drivers who have come in this week, worked their hearts out and really risen to the occasion, I would like to say a big thank you. I am very proud of the feedback you have generated," he said.
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