Erdogan promised the government will "not let down our people." He said by killing dozens of civilians, including women and children, the terrorists were not true Muslims.
"This is not Islamic. Taking one person's life means going straight to hell," he said Wednesday from the capital of Ankara, adding, "No terrorist organization will come between what we are."
Erdogan's televised comments came a day after he said in a written statement that an attack during the final days of the holy month of Ramadan show the attackers had no regard for faith or values.
No terror group has taken responsibility for the attack, in which three men arrived by taxi at the international terminal and launched their horror armed with rifles and suicide bomb vests.
Speculation, based on the nature of the attack, has focused on the Islamic State, which has struck in Turkey before but rarely taken credit for those bombings.
Interior Minister Efkan Ala said "all information and evidence" points to ISIS. "But nothing is for certain."
Prime Minister Binali Yildirim said initial findings "suggest all three attackers first opened fire then detonated themselves."
ISIS has a history of airport attacks. In March, it claimed responsibility for dual suicide bombings at the main airport in Brussels
, Belgium. At least 10 people died in those blasts.
And just like the Brussels attack, the terrorists in Istanbul took a taxi to the airport.
The Istanbul taxi driver was interviewed by police and released, the Turkish state news agency Anadolu reported.
The director of the U.S. Central Intelligence Agency, using another acronym for the Islamic State, said he thinks the terror attack "certainly bears the hallmarks of ISIL's depravity."
John Brennan said he wasn't surprised that ISIS hasn't said it was responsible. The group rarely takes credit for attacks in Turkey.
"I think what they do is they carry out these attacks to gain the benefits from it in terms of sending a signal to our Turkish partners," he told an audience at the Council on Foreign Relations in Washington, "(and at) the same time not wanting to potentially maybe alienate some of those individuals inside of Turkey that they may still be trying to gain the support of."
Victims from around the world
The death toll is now 42, according to Anadolu, which cited hospital sources. The toll rose after a woman died at a hospital in Istanbul.
Many of the dead were Turkish, including 10 airport staff members, TAV Airports CEO Sani Sener said.
The attack killed six Saudis and wounded 27 more, the Saudi Arabian Foreign Ministry said.
The other victims included two Iraqis, one Tunisian, one Chinese, one Iranian, one Ukrainian, one Jordanian and one person from Uzbekistan, a Turkish official said. Three of the foreigners had dual Turkish citizenship.
Of the 239 people wounded Tuesday night, 128 remained hospitalized, officials said.
The three terrorists
The assailants have not been identified, but there is a "strong suggestion that they are foreign," a senior Turkish government source told CNN.
Experts say Turkey is especially vulnerable due to the variety of terrorists operating there.
"You cannot protect these airports 100% ... especially in a place like Turkey, where ISIS has cells everywhere," said retired Lt. Col. Rick Francona, a former U.S. military attaché in Syria.
ISIS promised an uptick in attacks during the holy month of Ramadan, which is nearing its end.
And the terror group has reason to detest Turkey: The country is helping the U.S.-led coalition attack ISIS targets in neighboring Iraq and Syria. Turkey allows coalition planes to fly raids from its territory.
Adding to the instability: Last year, Turkey resumed hostilities with the PKK, Kurdish militant separatists, after a two-year cease fire broke down.
But over the last few months, "the Turks have really changed their focus from only the PKK to going after ISIS as well," Francona said.
Airport reopens quickly
Just five hours after terrorists struck, travelers returned to the site of the carnage -- much to the surprise of some critics.
"I find this totally astonishing," said Professor Larry Kobilinsky of the John Jay College of Criminal Justice. "I've never seen such a massive crime scene looked at for five hours. It's just impossible. You're going to compromise, you're going to contaminate evidence. ... They should not have turned this open to the public."
Passengers walked over shards of glass as workers tried to wash away blood at Ataturk Airport.
But the airport's operator defended its actions and its security, saying it exceeds international standards.
And unlike many American and European airports, "We have security checkpoints at the entrance of the terminal building," Sener said.
Those extra measures didn't stop the bombers, who started firing high-powered rifles immediately after getting out of a taxi, Sener said.
Despite the horror and carnage, "Everything's quite calm right now, which is a little surreal as opposed to the scenes we saw here last night," witness Laurence Cameron said.
"I was in the airport this morning looking for my lost luggage," he said. "They were sweeping up debris, and someone had hung up a big Turkish flag, pretty much right at the spot where (a) bomb had gone off -- sort of an act of defiance, which was quite moving."
, director of the Turkish Research Program at the Washington Institute, said he believes the attack was designed to hurt Turkey's tourism industry, which brings in more than $30 billion in revenue per year, according to its government.
"I think this was a deliberate effort on behalf of the Turkish government to give a message outside," he said of the airport's reopening.
"Because if ISIS, by carrying out the attack, tried to undermine Turkey's image as a place that's safe for business and safe for visitors, by getting the airport up and running and functioning in less than a day after the attack, Turkey's basically saying, 'Never mind, this was just a lapse, we're back in business.'"
A few shops inside the airport remained closed Wednesday, but for the most part the terminal where the attack took place was open. The only area that was closed was where one of the bombs went off. It was cordoned off by boards with advertisements on them.
There was a memorial in front of one food stand, a black table covered with roses and a photo of two of Tuesday's victims.
Lots of blood, broken glass
The cacophony of gunfire Tuesday night was quickly followed by the deafening blows of three explosions.
Witness Sue Savage said about 30 people were herded into a women's prayer room until authorities led them out and down an escalator into the main terminal hall.
"There was a lot of blood," she said. "There was so much glass on the floor, they were scuffing it aside so we didn't slip."
Video from inside the terminal shows the bright orange flash of fire from one of the explosions. Victims stagger. Some fall on the slippery, blood-covered floor.
Another video shows a gunman dropping his weapon when he's apparently shot by a security officer. The man slumps to the ground, and the officer briefly stands over him before running.
About 10 seconds later, a bomb detonates.
8 attacks so far this year
Turkey has spent much of this year reeling from terror attacks as it weathers bombing campaigns by both ISIS and Kurdish militants.
The attack marked the eighth suicide bombing event in Turkey this year. At least 140 people have been killed.
The violence has also rattled Turkey's tourism industry, a key sector of the national economy. About 39.4 million people visit each year.