Drone operators have deliberately targeted Gatwick Airport, causing chaos for more than 120,000 people just days before Christmas.
The military has been called in after the perpetrators escaped capture for more than 22 hours.
No indication has been given about when the UK's second busiest airport can reopen and easyJet has cancelled all flights to and from the West Sussex airport on Thursday.
The incident led to calls for more action to tackle illegal drone use.
The runway has been closed almost constantly since two drones were spotted being flown inside Gatwick's perimeter at 9pm on Wednesday.
It was reopened at 3am on Thursday but was closed 45 minutes later after the drones re-emerged.
Police described the devices as "industrial" models and are treating the incident as "a deliberate act to disrupt the airport".
Defence Secretary Gavin Williamson told reporters: "Sussex Police have requested assistance and support from the Armed Forces, and we will be deploying the Armed Forces to give them the help that they need."
Although he declined to specify what assistance would be offered, he said: "The Armed Forces have a range of unique capabilities and this isn't something we would usually deploy, but we are there to assist and do everything we can so that they are in a position to open the airport at the earliest possible opportunity."
Some 110,000 people were due to either take off or land at the airport on 760 flights on Thursday.
About 10,000 passengers were affected on Wednesday night.
Gatwick chief executive Stewart Wingate said he was "not in a position to say when it will be safe to reopen the airport".
Disruption will continue into Friday, which is one of the airport's busiest days of the year because of the Christmas getaway.
Mr Wingate said: "This is a highly targeted activity which has been designed to close the airport and bring maximum disruption in the run-up to Christmas."
He added: "We are still receiving drone sightings in and around the Gatwick airfield."
An emergency Whitehall meeting was held in response to the escalating crisis.
Transport Secretary Chris Grayling described the drones misuse as "quite clearly a deliberate act".
He told the BBC: "I have a very clear message to give to whoever's doing this – there's a five-year jail sentence for this kind of action and anyone who's doing this should expect to go to jail for many years."
Earlier this year, new laws came into force which ban all drones from flying within one kilometre of airport boundaries.
Drone users who flout the restriction face an unlimited fine, up to five years in prison, or both.
Mr Grayling said there was no known motive for the pilot of the "commercial" drone.
Night-flight restrictions will be lifted at other airports – probably those which serve London – so that "more planes can get in to and out of the country".
"Apologies for the residents affected, but it's right and proper that we try and sort people's Christmases out," Mr Grayling told Sky News.
Labour's shadow transport secretary Andy McDonald accused the Government of being "too slow to act" on drones and urged ministers to "fast-track the introduction of a regulatory framework".
Passengers faced severe disruption as flights were unable to leave the tarmac at Gatwick, while many inbound flights were diverted to alternative airports as far away as Amsterdam and Paris.
Some people reported being left stuck on planes for several hours while they waited to find out what was going on.
Lyndsey Clarke, from Southend, said she was on a stationary plane for more than four hours after it was re-routed to Stansted.
The 27-year-old said passengers were having to get taxis back to Gatwick after they were finally allowed off the aircraft.
Luke McComiskie's plane ended up in Manchester, and he described chaotic scenes as people tried to find their way home after more than three hours stuck on board.
The 20-year-old, from Aldershot, told the Press Association: "We got told there would be some arrangements with coaches for us when we get out the terminal ... It was just chaos and they had only two coaches and taxis charging people £600 to get to Gatwick."