Weather forecasters said the UK was still largely covered by the cloud of ash from the eruption in Iceland.
British Airways, bmi, Flybe and Ryanair had already cancelled all of their scheduled flights for Monday.
Thousands of Scots are still stranded abroad. The disruption is costing the travel industry millions of pounds.
Some scientists have warned the eruption from the Eyjafjallajoekull volcano could continue for months.
The Scottish government said it was working to deliver additional rail, bus and ferry services to aid passengers, and in discussions with UK ministers and the aviation authorities to find a solution as soon as possible.
Finance Secretary John Swinney told BBC Scotland's Politics Show he was concerned about the disruption, adding: "I think the economic impact is very significant and it is happening already."
A spokesman for National Air Traffic Services (Nats) said: "The volcanic ash cloud from Iceland shows continued and extensive cover of the UK.
"We will of course continue to make best use of any breaks in the ash cloud to offer opportunities to airlines as they arise."
Passengers have been urged not to travel to airports until further notice, and to remain in contact with their airlines.
All airlines at Glasgow Airport have cancelled their entire schedules for Monday.
A statement released by Glasgow Airport said: "We appreciate the continued patience of passengers at this difficult time and will provide updates as often as possible."
More than 100 soldiers arrived home in Edinburgh from a six month tour of Afghanistan on Sunday after spending the last few days in Cyprus.
The members of B Company, 1st Battalion the Royal Regiment of Scotland, had originally been due to arrive home at lunchtime on Friday.
They were flown into France on Saturday and spent the night travelling overland by coach and ferry.
In the Western Isles, a 34-year-old woman was flown by Stornoway Coastguard Rescue Helicopter to Glasgow's Southern General Hospital, after experiencing complications with her pregnancy.
Brian Potter, president of travel agents body the Scottish Passenger Agents' Association, said the situation was "chaotic" for the thousands of Scots who are unable to get home from foreign airports.
Travel agents had staff working overtime all weekend in an effort to bring people stranded abroad home, Mr Potter said, but he warned that with trains and ferries already fully booked it could be at least Thursday or Friday before many people were repatriated.
Mr Potter told BBC Scotland individuals stuck overseas were having to pay their own hotels most of the time and had to read their insurance small print carefully and check what is covered as either an act of God or under bad weather.
He said the disruption was also "devastating" for airlines and travel companies.
"Every day that it continues is more and more worrying for all the airlines who are not making money," he added.
"The whole travel trade is fighting against this more than anything they have done ever before. There has never been anything quite like this - it is a one-off situation."
A Polish man who has been stuck at Glasgow Airport for two days told BBC Scotland he felt he could not leave in case a flight became available.
Piotr, 38, said: "This is not a problem for me to stay here two nights, three nights."
Tony Followell, from Glasgow, was among a queue of stranded people trying to board a P&O ferry from Bilbao in Spain to Portsmouth on Sunday morning.
He said: "It seems there are a lot of people who have arrived on spec by train from places like Barcelona and Madrid overnight.
"I know one couple had flown from Majorca into Barcelona and taken a train across to Bilbao to get the ferry home.
"There are a number of people in the waiting queue - and it is probably a couple of hundred - hoping to get on this morning's ferry. I doubt very much whether they will make it."
Graeme Leitch of the Met Office said a change in the wind direction might mean flight restrictions could be lifted, but there was no indication that any such change was imminent.
Restrictions on Scottish airports had been been lifted briefly on Friday before being quickly re-imposed as the cloud changed shape and direction.
A British Airways flight from New York and a Thomas Cook flight from Orlando were allowed to land at Glasgow Airport on Saturday morning.
Dust from the cloud has fallen to the ground in some areas of Scotland, but the Scottish Environment Protection Agency has said it does not pose a risk to health.