Officials believe the men -- identified by state media as being from Russia, Uzbekistan and Kyrgyzstan -- entered Turkey about a month ago from the ISIS stronghold of Raqqa in Syria, bringing with them the suicide vests and bombs used in the attack, the source said.
The terrorists rented an apartment in the Fatih district of Istanbul, where one of the attackers left behind his passport, the Turkish government source said.
The attack was "extremely well planned with ISIS leadership involved," the source said.
Turkish police visited the Fatih area and showed neighbors video and photographs of three men they say are believed to have carried out the attack, residents said.
Among the pictures was a screen grab from surveillance video at the airport that shows three men wearing thick jackets and carrying bags, the residents said. One man, the owner of the Bekir Yar Emlak real estate agency, said he told police that the picture showed the men who had lived in his apartment. He said he was shocked to learn they could be the suspects.
Mustafa Elsan, the owner of a garage next to the apartment building, also said he was shown images of the alleged attackers. Elsan said he would see people smoking by the window of that apartment on the first floor of the building, but the curtains were mostly closed.
A female neighbor in the same building, who didn't want to disclose her name, said there was some smell of chemicals a couple of days ago from the apartment, prompting other neighbors to ask her whether there was a gas leak.
Death toll climbs
The death toll rose to 44 when a 3-year-old Palestinian boy hurt in the attack died, according to Palestinian officials. The boy's mother died Wednesday, officials said. And Turkish state news agency Anadolu reported a Turkish man died at a hospital.
While no one has yet claimed responsibility for the airport assault
, CNN contributor Michael Weiss, author of "ISIS: Inside the Army of Terror," said the nationalities revealed Thursday buttress the claim of ISIS involvement.
"One of the toughest battalions in ISIS is called the Uzbek battalion," he said. "These were the guys who were essentially on the front lines guarding Falluja, the city they just lost in Iraq."
"Ask anybody inside ISIS or who's fought ISIS. People from the former Soviet Union tend to be the most battle-hardened and willing to die," he said.
CNN national security analyst Peter Bergen said the revelation of the Istanbul attackers' nationalities will serve to "open people's eyes to the fact that there's a very substantial Russian, former Soviet Union, presence within ISIS, both in terms of the foot soldiers and the leaders."
Estimates of Russian fighters involved with ISIS range from 2,000 to 7,000, he said.
Kyrgyzstan's foreign ministry disputed reports that one of the attackers was from that country.
The ministry said Turkish officials told its representatives that "the identities of the suicide bombers are still being examined."
Suspects detained in attack probe
Also Thursday, authorities detained 22 people in connection with the attack, according to a Turkish official.
Thirteen were taken into custody in Istanbul and nine in the coastal city of Izmir, the official said. Three of those detained were foreign nationals, state media reported.
The terrorists stormed the airport Tuesday nigh
t, opening fire and detonating explosives -- two of them at the international terminal building, and the third in a parking lot, according to officials.
Like the attack in Brussels,
the terrorists took a taxi to the airport.
History of airport attacks
Preliminary findings suggest all three attackers at Ataturk airport opened fire and then detonated explosives strapped to their bodies, similar to the mass shootings and suicide bombings at Paris' Bataclan
concert hall in November. ISIS claimed responsibility for that massacre
, which left 89 people dead. Similar attacks took place elsewhere in Paris the same night, killing an additional 41 people.
The tactic -- to enter shooting, and then detonate explosives -- is called "inghimasi," and it's being used more and more frequently by terrorists.
"The 'inghimasi,' their (modus operandi) on the ground in Syria and Iraq, is to shoot up checkpoints and then they actually -- some of these guys actually run up to the enemy and hug them before detonating the bomb to take them out with themselves. So in a sense, the ultimate Kamikaze warrior," Weiss said.
ISIS also has a history of airport attacks. It claimed responsibility for dual suicide bombings at the main airport in Brussels
in March. At least 10 people died in those blasts.
The CIA director said the terror attack mirrors similar ones by ISIS.
"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 ... 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," John Brennan said.
Victims from all over the world
Those killed at the Istanbul airport had come from all over the world, but most of them were Turkish, including 10 airport employees, TAV Airports CEO Sani Sener said.
Saudi Arabia's foreign ministry said six Saudis were killed and dozens more wounded.
Other fatalities 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.
One U.S. citizen suffered "minor injuries," Homeland Security Secretary Jeh Johnson said Thursday.
The Islamic State has struck in Turkey before, but has rarely taken credit for those bombings.
Experts say Turkey is especially vulnerable because various terrorists operate there.
ISIS has a 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 list of enemies, Turkey resumed hostilities with the PKK -- Kurdish militant separatists -- last year after a ceasefire broke down.
Turkey has spent much of this year reeling from terror attacks as it weathers bombing campaigns by both ISIS and Kurdish militants.
The airport attack marked the eighth suicide bombing 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.