BRUSSELS - Airlines cancelled hundreds of flights and European railways froze links with Brussels Tuesday after rush-hour bomb attacks killed around 35 people in the city's airport and a metro train, sparking a broad security response.

Belgium locked down the capital, home to the headquarters of the European Union and NATO, and imposed its highest level of security alert after the explosions, which killed about 14 people in the airport and another 20 in the metro, according to authorities in Brussels.

As passengers fled the smoking airport and the city-centre Maalbeek metro station, transport operators shut down the airport, metro system, buses, trams and major railway stations in the capital.

"Our whole network is closed at the moment," the Brussels public transport operator STIB warned people on Twitter, confirming the closure of metro, bus and tram systems. Major railway stations were closed, too, the Brussels public prosecutor said.

Eurostar said all trains to and from Brussels had been halted. "Our thoughts rest with anyone affected by the unfolding events in Brussels," it said in a statement.

The high speed train service Thalys, which links France and Belgium, said its traffic, too, had been stopped.

The Brussels-Zaventem international airport was closed until 6am (0500 GMT) Wednesday, the airport said.

"All flights cancelled at #brusselsairport for the rest of the day. Avoid the surroundings of the airport," the airport said on Twitter. "All our thoughts go to the victims of the horrible events that happened here at #brusselsairport this morning, their family and friends."

The airport shutdown forced more than 500 arrivals and departures to be cancelled or diverted, according to the European Aviation Crisis Coordination Cell in Brussels, paralysing air links with cities across Europe and other international airports.

Belgium's crisis centre urged people not to move. "No public transport. Stay where you are, also in schools, companies," it said on Twitter.

National forces tightened security at nuclear plants across Belgium, the Belga news agency said. "Vehicles are being checked with police and army on site," the agency added.

Belgium's neighbours France, Germany and the Netherlands reacted swiftly.

In France, where the November 13 Paris attacks that killed 130 people were intricately linked to jihadist networks in Belgium, an additional 1,600 police were deployed to border crossings, airports, ports and train stations, said Interior Minister Bernard Cazeneuve.

People in France will need tickets or ID cards to access public transport areas, he said, and they may be frisked. Armoured cars were positioned at Paris' Orly and Roissy airports.

French Prime Minister Manuel Valls said it was time to adopt legislation obliging airlines to hand their passengers' data to European Union countries, a proposal that has raised privacy concerns. "We have lost enough time on this," he said.

Bus services between France and Belgium were cancelled or disrupted, companies said.

In Germany, federal police said controls were being stepped up at the border with Belgium and at airports and stations. Frankfurt airport raised security.

The Netherlands, likewise, strengthened surveillance at the border with Belgium and ordered extra police patrols at Amsterdam's Schiphol international airport, Rotterdam and Eindhoven.

Elsewhere, London Gatwick, Barcelona and Moscow airports raised security, too.

Moscow beefed up security over "a heightened terror threat in Russia", a senior member of the senate committee for defence and security told RIA Novosti news agency.

Across the Atlantic, police in New York said they were positioning counter-terrorism reinforcements to crowded areas and train stations "out of an abundance of caution". In Washington DC, canine sweeps and patrols and patrols were stepped up, also as a precaution.