The Jersey-based operator, which employed around 100 people, announced on Friday that it had ceased trading and cancelled all bookings.
Carl Walker, chairman of the Jersey Consumer Council, said they learned that more than 1,000 passengers had been displaced and that advice had been issued to affected customers.
Aurigni and Loganair said they were launching additional flights to assist Blue Islands customers.
Loganair said it was resuming flights from Jersey to Guernsey, Exeter, Bristol, and Southampton, as well as from Guernsey to Southampton, starting Sunday, while Aurigny has resumed flights on the Southampton to Guernsey and Guernsey to Jersey routes "initially until Wednesday."
Both airlines said special rescue fares were being implemented on flights to assist passengers traveling on affected routes.
A statement from Loganair said: "We understand this will be a worrying time for those hoping to travel to and from Jersey, and in light of this, we are resuming operations from Sunday, November 16."
A spokesperson for Aurigny said the airline was "deeply saddened" by Blue Islands's closure and had taken "immediate action to assist Blue Islands customers in the Channel Islands."
Loganair Chief Executive Officer Luke Farajallah said Blue Islands played a "vital role in the UK regional aviation market."
He said, "Coming so soon after the news from Eastern Airways, this is another sad day for regional aviation."
Mr. Farajallah said Loganair took immediate action to resume flights to and from Jersey, opening up the possibility of the airline becoming a long-term operator for the island.
In a statement discussing the additional flights, they said: "Following this, a new permanent operations hub will be established in Jersey."
Jersey Airport Operations Director Ashley Maggs said the situation is frustrating, but they are working to ensure that travellers are not displaced.
He said, "Our thoughts are with the staff and employees of Blue Islands, our partners who have been affected by this incident - serving Jersey has been a great achievement for them and this is very sad news."
Mr. Maggs said they are in talks with Loganair to ensure operations continue smoothly from Sunday.
He said: "There is no emergency; we are simply working with them to address the shortcomings."
Mr. Maggs said staff worked overnight and the situation is progressing well, so "two of our flights should be operating tomorrow."
Blue Islands passengers John and Maureen Stranger said they were scheduled to fly to Southampton on Saturday after attending a school reunion in Jersey.
Mr. Stranger said they managed to book a British Airways flight to Gatwick after learning about the Blue Islands collapse while watching the news at 11 p.m. on Friday.
"It took me about three hours to sort it out," he said.
"I was very sad when I found out, and my wife asked, 'Well, how are we going to get home?'"
Mrs. Stranger said the couple were "shocked and devastated" by the tragedy.
"The hotel management helped us a lot," she added.
"They stayed up late to help us."
David and Anne Patterson, who were in Jersey visiting a relative, said they were scheduled to fly to Southampton on Blue Islands on Tuesday.
The couple said they were "a bit shocked" to hear the news of the airline's closure and sympathize with its employees.
Mr. Paterson said they managed to book a Loganair flight to Southampton on Tuesday.
He added, "Actually, this is getting us to Southampton 15 minutes earlier than other airlines."
"If my friend John is watching this program, I'll be arriving earlier!"
A 'limit' on subsidy
A statement issued by Blue Islands said they were informed on Friday that the Jersey government would not be able to provide any further assistance.
A spokesperson said: "This means we must now immediately suspend flights while we consider the available options and how we can support our customers, employees, and stakeholders."
Blue Islands had borrowed £8.5 million from the Jersey government to help preserve its services during the COVID-19 pandemic.
A report in August showed that the outstanding capital balance in June was £7 million.
Jersey's Finance and Resources Minister, Elaine Miller, said it was very sad news for the island, but there was "a limit" to how much the government could subsidize an airline.
'Passengers are the priority now'
Ports of Jersey said they were saddened by the news: "Blue Islands has been a significant operator at Jersey Airport for many years."
"We recognize this news will be disappointing for passengers, staff, and the wider island community," a statement said.
Guernsey Ports Managing Director Ross Coppolo said he hoped rescue flights with airlines such as Aurigny and Loganair would help minimize disruption.