British Airways has frozen recruitment
Airlines worldwide have been badly hit by the impact of Tuesday's tragic events, with US carrier Continental cutting 25% of its flights and giving 12,000 staff a leave of absence.
British Airways has introduced a recruitment freeze as it faces increased costs for security, lower demand for flights and the knock-on effect of cancelled flights in recent days.
Last year BA's transatlantic operations accounted for more than a third of its £9.3 billion revenue.
In the wake of the attacks BA saw its share price dip to 165p - earlier in the year shares had been trading as high as 463p. Earlier in the year BA announced 1,800 job cuts from its 62,000 global workforce.
Unions had already been expecting around another 2,000 job losses but now fear the final figure will be much higher.
And a report in the Sunday Business estimated that the firm could shed 6,000 jobs.
A BA spokeswoman said it was too soon to be talking in detail about the effect the US attacks would have.
"Obviously under the circumstances and as a responsible company there are things we are doing such as tightly managing our expenditure.
"But it is important to be calm and considered, to make sure the business gets through okay," she said.
Review
Virgin Airways and British Midland have both said they are monitoring the situation but stressed job cuts were not currently being considered.
Virgin said a review has been ongoing since the attacks, but that no decisions had yet been taken.
A spokesman for British Midland said: "We've not noticed a dramatic change in flight traffic on our (non-US) flights since the tragedy."
He said passengers had been offered refunds on flights since Tuesday but there had been a "very small" uptake.
"We carry a lot of business passengers and I expect it will be the leisure industry that is worst hit in the short term."
Analysts believe that any long-term changes in security measures at airports could hit budget carriers, which rely on a quick turn-around of passengers to keep costs low.