The suspension of takeoffs from runway 27L of Britain’s busiest airport was announced shortly before 6pm on Tuesday.
Chris Grayling, the transport secretary, said he was prepared to deploy the same anti-drone military technology used at Gatwick if needed.
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A Heathrow airport spokesperson said during the shutdown that they were “responding to a drone sighting at Heathrow and are working closely with the Met Police to prevent any threat to operational safety.
“As a precautionary measure, we have stopped departures while we investigate.
“We apologise to passengers for any inconvenience this may cause.”
Monitoring app FlightRadar24 showed planes continuing to land at the west London airport during the closure.
Mr Grayling said he was in contact with the home secretary and defence secretary and “the military are preparing to deploy the equipment used at Gatwick at Heathrow quickly should it prove necessary”.
The Metropolitan Police said in a statement they had “received reports of a sighting of a drone in the vicinity of Heathrow airport”.
The force added: “As a precautionary measure, Heathrow airport has stopped departures and officers based at Heathrow are currently investigating the reports with colleagues from airport.”
Flights began taking off around 20 minutes later, FlightRadar24 showed. A KLM 737 bound for Amsterdam was one of the first to leave after the runway was reopened.
A statement from the airport said: “We continue to work closely with the Met Police to respond to reports of drones at Heathrow.
“Based on standard operating procedures, working with Air Traffic Control and the Met Police, we have resumed departures out of Heathrow following a short suspension.
“We continue to monitor this situation and apologise to any passengers that were affected by this disruption.”
The temporary disruption came after days of delays and cancellations at Gatwick following multiple reports of one or more drones flying over the runway before Christmas.
The West Sussex airport was repeatedly forced to close between 19 and 21 December affecting around 1,000 flights.
In response the government has announced a package of measures which include plans to give police the power to land, seize and search drones.