EasyJet has said it is introducing "further significant cancellations" as a result of travel restrictions caused by the coronavirus pandemic.
The airline said in a statement: "Due to the unprecedented level of travel restrictions being imposed by governments in response to the coronavirus pandemic and significantly reduced levels of customer demand, easyJet has undertaken further significant cancellations.
"These actions will continue on a rolling basis for the foreseeable future and could result in the grounding of the majority of the easyJet fleet.
"EasyJet will continue to operate rescue flights for short periods where we can, in order to repatriate customers."
British Airways' parent company IAG also announced plans to reduce capacity.
It said in a statement: "IAG is implementing further initiatives in response to this challenging market environment.
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"Capacity, in terms of available seat kilometres, in the first quarter of 2020 is now expected to be reduced by around 7.5% compared to last year.
"For April and May, the group plans to reduce capacity by at least 75% compared to the same period in 2019.
"IAG is also taking actions to reduce operating expenses and improve cash flow. These include grounding surplus aircraft, reducing and deferring capital spending, cutting non-essential and non-cyber related IT spend, freezing recruitment and discretionary spending, implementing voluntary leave options, temporarily suspending employment contracts and reducing working hours."
Travel company Tui said: "In this rapidly changing environment the safety and welfare of our guests and employees worldwide remains of paramount importance and thus Tui Group has decided, in line with government guidelines, to suspend the vast majority of all travel operations until further notice, including package travel, cruises and hotel operations.
"This temporary suspension is aimed at contributing to global governmental efforts to mitigate the effects of the spread of the Covid-19."
Transport Secretary Grant Shapps said there are "lots of different options" to help the aviation industry through the coronavirus crisis.
He told Sky News: "We want to make sure that companies and individuals and organisations who are in a good state – not those that are going to fail anyway – are able to continue.
"So, we'll be looking at all of these measures, I'll be discussing it with the Chancellor and the Prime Minister later today, and those discussions with the sector are ongoing."
Asked if a bailout of airlines was on the table, Shapps said: "There are lots of different options here - including some other things that people have been looking for, for example HMRC offer a 'time to pay'."
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Shapps described the spread of coronavirus as an "international crisis".
He told BBC Breakfast: "This is no doubt at all, there is no sugar coating this. This is obviously an international crisis and we need a great national effort to help everybody in society get through this. But we will get through it. We will beat this virus, but there is no shortcut unfortunately to getting there."
Shapps said the Government's approach was driven by science and evidence.
"I don't think that necessarily means that our approach is markedly different... but I do think it means that we deploy each of these different measures at the appropriate time."
He added: "We're not doing the things that sometimes perhaps are happening elsewhere because it seems like a popularist thing to do, we want to know that the scientists back it and that is, I suppose, the hallmark of this country's response."
He also said the UK's outbreak is behind that of other European countries, telling Sky: "The UK has probably just been at a slightly different stage - compared with places like Italy but also a little behind where France and Germany are.
"It's not that we're not going to get there, but of course our responses are timed in a different way, unique to the particular stage of this that we're in in the UK."
As more countries impose restrictions on travel and airlines continue to cancel flights, he advised Britons stuck abroad to make themselves known to the Foreign Office.
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