Witnesses described scenes of terror and panic on Tuesday evening as the attackers began shooting indiscriminately and then blew themselves up at the entrance to Ataturk airport, one of Europe's busiest hus.
The assault, which comes at the start of Turkey's crucial tourist season, was the latest in a wave of attacks in Istanbul and the capital Ankara blamed either on Islamic State (IS) jihadists or Kurdish rebels.
Interior Minister Efkan Ala said there was an ongoing "serious and comprehensive investigation" into who was behind the attack, using another name for IS as he told reporters: "First signs point to Daesh but it's not certain yet."
CIA director John Brennan also said the attack bore the "hallmark" of the jihadist group.
The death toll is now 42, according to Turkish news agency Anadolu, which cited hospital sources.
The toll rose after a woman died at a hospital in Istanbul on Thursday.
The dead include several Saudis, a Chinese national, a Tunisian and a Ukrainian.
The carnage sparked global condemnation, with US President Barack Obama speaking by phone with his counterpart Recep Tayyip Erdogan to express his condolences.
Erdogan declared Wednesday a national day of mourning after urging an international "joint fight" against terror.
Security camera footage widely circulated on social media appeared to capture two of the blasts. In one clip a huge ball of flame erupts at an entrance to the terminal building, scattering terrified passengers.
Another video shows a black-clad attacker running inside the building before collapsing to the ground -- apparently felled by a police bullet -- and blowing himself up.
The attack came just as Turkey, which had found itself increasingly friendless on the international stage, begins rebuilding relations with Israel and Russia.
It also follows coordinated IS suicide bombings at Brussels airport and a city metro station in March that left 32 people dead.
Obama appeared to back the theory that IS carried out the Istanbul attack, telling reporters in Canada: "It's an indication of how little these vicious organisations have to offer beyond killing innocents."
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'Let me see my child'
Women sobbed outside a local morgue, while families were desperately waiting for news of loved ones outside several Istanbul hospitals.
"Let me see him, I beg you," a woman screamed outside one hospital. "No one's told me what's happened to my child. I raised him. They're not telling me anything."
Diplomats in Tunis said Fathi Bayoudh, a Tunisian killed in the attack, had travelled to Turkey to secure the release of his son who was detained for joining IS, the country's private Mosaique FM radio reported.
The airport itself was back up and running by early Wednesday, with workers clearing up the shattered glass and nervous passengers filing in as flights resumed.
"I felt very anxious coming to the airport," Irish tourist Steven Parkinson told AFP.
"You hope obviously that something like that, it won't happen two days in a row again, that there is a lot of security -- but obviously it affects you."
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Prime Minister Binali Yildirim told a press conference in Ankara late Wednesday that Turkey would "increase the presence of specially-trained staff" at the nation's airports.
South African university administrator Judy Favish said she had hidden under a counter as the attackers opened fire.
She and other travellers were ushered to the basement before emerging about two hours later.
"We walked through the airport and saw debris and blood. It was just chaos," she told South African TV network eNCA.
'Walking like a prophet'
An AFP photographer saw bodies covered with sheets at the terminal, where bullet holes peppered the windows and shattered glass was strewn on the floor, along with abandoned luggage.
Otfah Mohamed Abdullah was checking her luggage in when she saw one of the attackers pull out a hidden gun.
"He's shooting up, two times, and he's beginning to shoot people like that, like he was walking like a prophet," she told AFPTV.
"Everybody started running in different directions when the shooting started. I hid under the counter where I was standing and a couple of the ground staff did the same," South African university administrator Judy Favish told eNCA television in her home country.
Favish said she and other travellers were ushered to the basement before emerging about two hours later.
"We walked through the airport and saw debris and blood. It was just chaos. It was horrible."
'Declaration of war'
Analyst Soner Cagaptay, director of the Turkish Research Programme at The Washington Institute, described it as a "symbolic attack against the heart of Turkey".
"If this Islamic State is indeed behind this attack, this would be a declaration of war. Turkey's vengeance will come down like rain from hell on the Islamic State."
The attack prompted the suspension of all flights at the airport, but operations were resuming on Wednesday with some delays.
There was chaos at the nearest hospital in Istanbul's Bakirkoy district, which was inundated with relatives desperate for news of loved ones.
Brussels airport, the scene of suicide bombings just months ago, tweeted condolences, saying: "Our thoughts are with the victims of the attacks at @istanbulairport.".
The US and French consulates warned people to stay away from the area.
Erdogan met his prime minister and military chief after news of the carnage broke.
"We urge the world, especially Western countries, to take a firm stand against terrorism," Erdogan said in a statement.
"Despite paying a heavy price, Turkey has the power, determination and capacity to continue the fight against terrorism until the end."
Tourism targeted?
Tourism, a key source of income in Turkey, has been badly hit by a spate of deadly recent bombings.
The government will be hoping to recoup some of the losses after Russia on Wednesday lifted punishing sanctions imposed over a diplomatic spat, including a ban on package holidays.
But Ege Seckin, an analyst at IHS Country risk, said the attack was "most likely conducted by the Islamic State to undermine the Turkish economy by attacking the airport ahead of the summer months, when tourism peaks".
The country has been hit by at least five attacks blamed on IS jihadists, including a blast in Ankara in October that left over 100 dead, the worst in the country's modern history.
In January, a bombing in the heart of Istanbul's tourist district, also blamed on IS, killed a dozen German visitors.
Two months later, three Israelis and an Iranian were killed in another attack attributed to the jihadists on the city's main Istiklal shopping street.
The Kurdistan Freedom Falcons (TAK) -- seen as a splinter group of the rebel Kurdistan Workers' Party (PKK) -- also claimed a car bombing in Istanbul in June that killed 11, and warned foreign tourists they were not safe.
The group said it was avenging Ankara's sustained offensive against the outlawed PKK in southeastern Turkey following the collapse of a ceasefire last year.
Hundreds of members of the Turkish security forces have since been killed in PKK attacks.
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