More than 120,000 passengers have been affected by delays and cancellations, with all flights grounded for at least 33 hours as the Christmas getaway begins.
The drone or drones first appeared at 9pm on Wednesday and by Thursday night there had been 50 reported sightings. The airport is not due to open before 6am on Friday.
Sussex Police said they were trying to identify the make and model of the flying machine and were actively considering shooting it down.
Detective Chief Superintendent Jason Tingley said the use of firearms “will be within our suite of tactical options available to us going forward”.
He added: “One of the options is to use firearms officers if that presents itself – they have been out on the ground today and that’s a consideration and a tactical option that is open to us.
“There are a number of factors in terms of range, the height of the drone and the likely impact of us firing at the drone but that is a tactical option open to the gold commander who will make a decision based on the information available to them at the time.”
Chris Woodroofe, Gatwick’s chief operating officer, said the airport could potentially remain closed for all of Friday following further drone sightings.
He said: “My apologies to all those passengers who have seen this disruption from the criminal activity from these people who are purposely disrupting our airport and their travel so close to Christmas.”
“We have had the police, we have had the military seeking to bring this drone down for the last 24 hours and to date that has not been successful so Gatwick Airport is still closed.
The government, which condemned the activity as as “incredible irresponsible”, is facing widespread calls for the urgent introduction of stronger drone laws.
Transport Secretary Chris Grayling said there was no known motive for the drone activity but said there was no suggestion it was related to terrorism.
To read our coverage of developments as they happened, see below
Please allow a moment for this live blog to load
Good morning and welcome to The Independent's live coverage as drones reported flying near to Gatwick cause travel chaos at the airport.
The airport's runway remains shut this morning, grounding outgoing planes and forcing diversions of incoming flights.
Flights in and out of the Gatwick were first suspended at about 9pm last night after two drones were sighted near the airfield.
Gatwick announced that the runway had reopened at about 3am today, but just 45 minutes later it was shut again following further sightings.
Here's our report from last night:
Chris Woodroofe, Gatwick's chief operating officer, said that further drones had been spotted over the airport as recently as 7am today.
He condemned the "irresponsible" activity, telling BBC Radio 4's Today that 10,000 people had been affected by the closure, including 2,000 whose flights had been unable to take off.
He said two drones were involved, and were seen flying "over the perimeter fence and into where the runway operates from".
Mr Woodroofe said: "They disappeared and reappeared over the night period from 9pm until 3am, at which point we reopened the runway.
"That lasted 45 minutes before the drones reappeared again and we are currently closed and it is our intention to review the situation when we have daylight at 8am."
Police do not want to shoot down the drones because they are concerned about stray bullets, Gatwick's chief operating officer.
Chris Woodroofe: "The police are looking for the operator and that is the way to disable to drone.
"We also have the helicopter up in the air but the police advice us that it would be dangerous to seek to shoot the drone down because of what may happen to the stray bullets."
Twenty police police units from two forces were hunting for the drone pilots.
Gatwick has issued a new statement on the disruption, advising passengers not to travel without first checking with their airline.
Flights into and out of the airport remain suspended, and no time has been given for its runway to be reopen.
Some passengers have reported spending most of the night in planes stuck on the runway at Gatwick.
Jeremy Taylor said he was "stuck on the tarmac for six hours trying to get to Buenos Aires" before spending two hours trying to get to a hotel.
He also criticised "minimal info", and tweeted a picture of crowds waiting the airport.
Drones spotted again at Gatwick
Drones have been seen again flying over Gatwick, according to the airport's chief operating officer.
Chris Woodroofe just told Sky News: "As I stand here there is a drone on my airfield, as we speak."
Aviation minister Baroness Sugg has issued a statement condemning the drone pilots, who she said are acting "incredibly irresponsibly" and could face prison sentences of up to five years. She said:
These drones have been flown illegally and the operators, who have acted incredibly irresponsibly, could face up to five years in jail.
We are in close contact with Gatwick Airport as they work with police to safely resolve the situation as quickly as possible.
The pilots of the drones disrupting Gatwick could be using technology that "mask their identity", an expert has said.
Berry Jenkins, director of counter drone strategy at Drone Major Group, told BBC Radio 4's Today programme: "There are ways of masking both your origin - where you've taken off from - and where you are in flight.
"So this is a challenge for the security forces on the ground and indeed the operating officer at Gatwick."
"Tougher laws and enforcement" are needed to prevent drones disrupting passenger flights, the British Pilots Association has said.
The organisation said drones could have could have "catastrophic consequences" if they collided with an aircraft, in a statement which shows why Gatwick are taking this so seriously.
The association's head of flight safety, Rob Hunter, said:
The public needs to understand that drones are not just toys and could have catastrophic consequences if they collide with an aircraft. We know a lot of drones will be under people’s Christmas trees and we implore them to ensure they’re aware of the rules and fly their drones in a safe and sensible manner.
These drone sightings at Gatwick are further evidence that tougher laws and enforcement are required to keep drones clear of manned flights. That’s why we need the registration and education process in force sooner rather than later, so people flouting the law can be caught and prosecuted.
He also called on the government to consider toughening the law to create a larger no-fly zone around airports.
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