Mourners in Brussels have kept an all-night vigil at a makeshift memorial in the Place de la Bourse, a square in the ancient heart of the city.
In New Zealand, meanwhile, there are plans to light the Sky Tower in Auckland and the Michael Fowler Centre in Wellington in the colours of the Belgian flag - black, yellow and red.
People light candles in tribute to victims at a makeshift memorial in front of the stock exchange at the Place de la Bourse in Brussels. Photo: AFP
Belgium is observing three days of mourning following bomb attacks in the capital that left 34 people dead and about 250 wounded.
A minute's silence for the victims will be held at midday local time (midnight tonight NZT).
Police are continuing a huge manhunt for a suspect caught on CCTV shortly before two bombs exploded at Zaventem airport on Tuesday morning.
An hour later another blast tore through a metro train near the Maelbeek station.
So-called Islamic State (IS) has said it was behind the attacks and warned that more would follow.
Listen to Brussels correspondent Jack Parrock
Meanwhile, the US State Department has urged US citizens of the "potential risks" of travelling to Europe.
A statement said terror groups were planning "near-term attacks throughout Europe, targeting sporting events, tourist sites, restaurants and transportation".
Tuesday's blasts came days after the capture in Brussels of Salah Abdeslam, who investigators say was involved in last November's terror attacks in Paris.
Abdeslam is due to appear before a pre-trial court in Brussels on Wednesday.
Hundreds of people crowded into Place de la Bourse late into Tuesday night, lighting candles and placing flowers in a vigil for the victims of the attacks.
Belgian Prime Minister Charles Michel, joined the vigil as night fell, said it had been "a day of tragedy, a black day" and urged citizens to show "calmness and solidarity".
Many cities around the world illuminated their landmarks in the colours of the Belgian flag in a show of solidarity.
Wellington mayor Celia Wade-Brown said the city would do the same with the Michael Fowler Centre, in a show of support for those affected.
SkyCity said the Sky Tower would also be coloured black, yellow and red.
World leaders have sent condolences and messages of solidarity.
US President Barack Obama called the blasts "outrageous attacks against innocent people" while the 28 EU leaders - in a joint statement - said the bombings were an "attack on our open, democratic society".
New Zealand Prime Minister John Key said the thoughts of New Zealanders were with the people and the government of Belgium.
"Atrocities like this and the recent attacks in Turkey are a stark reminder of why the international community must stand together in the global fight against terrorism.
"Our thoughts are with Belgians in the aftermath of this shocking attack."
Labour leader Andrew Little and Green Party foreign affairs spokesman Kennedy Graham also expressed their condolences for those killed.
Anti-terror raids across Belgium
Raids took place in Brussels and across Belgium on Tuesday as anti-terror police sought those linked to the attacks.
They issued a wanted notice for a man seen walking with two other suspects at the airport just before the blasts at a check-in hall.
He was pushing a luggage trolley with a suitcase thought to have contained a bomb that didn't explode. The two other men are presumed to have died after detonating suicide devices.
Suspects caught on camera at Brussels Airport Photo: AFP / Federal Police / Belga Mag / Belga
The explosions happened in quick succession shortly after 8am local time (8pm NZT) and the other bomb was found and destroyed in a controlled detonation.
A taxi driver who had reportedly driven the three suspects to the airport gave police an address in the Schaerbeek area of Brussels, where another explosive device and an IS flag were among items recovered.
Police helicopters hovered over the city late into the night as the search operation continued.
About an hour after the airport blasts on Tuesday morning, another explosion struck the Maelbeek metro station near EU headquarters.
The cause of the blast has not been confirmed but IS said it too was a suicide bombing.
Police said at least 11 people died on the metro train.
Belgium has raised its terrorism alert to its highest level.
Transport across Brussels was paralysed after the explosions but some services later resumed. The airport is unlikely to reopen for several days.
-BBC/RNZ