The troubled low-cost carrier announced earlier that it had applied for business liquidation, and that all of its flights had been cancelled.
Airports Company South Africa spokesperson Solomon Makgale told Fin24 that 13 1time flights were cancelled, leaving an estimated 2 000 passengers stranded in airports around the country.
But a 1time spokesperson, Refilwe Masemola, said that there is nothing the company can do for the passengers.
She said passengers must book a flight with another carrier, as 1time does not have the means to accommodate them.
Comair CEO Erik Venter said there was very little that his company could do to help either.
He said the timing was "unfortunate" as the seats of most other airlines had already been booked.
The DA, however, felt that South African Airways (SAA) should should do "everything it can" to assist 1time passengers by offering discounted flights, saying that continued generous support for SAA, SA Express and Mango was one of the causes for 1time's failure.
The party's spokesperson on public enterprises, Natasha Michael, said 1time's liquidations was "a blow to South African consumers and proof of the devastating effect of the anti-competitive behaviour of state-backed SAA".
"The DA strongly believes that the domestic airline market will continue to suffer until such time as the Competition Commission addresses the unfair competition and anti-competitive behaviour of state carriers that are able to rely on government bail-outs and are effectively subsidised to squeeze out independent players,” she said in a statement.
Comair's Venter echoed her sentiments, but said due to the less efficient fleet 1time operated, the ultimate closure of the airline was "inevitable".
"However, we are certain that in the absence of state-subsidised Mango, 1time would have made adequate profits to upgrade its fleet and be sustainable over the long term," he said.
Meanwhile, 1time CEO Blacky Komani said earlier that company officials are working to assist passengers with refunds.
"There is going to be a refund process," Komani said in a statement.