Turkish President Recep Tayyip Erdogan has vowed that his country "will never be divided" a day after suicide blasts killed at least 41 people and wounded nearly 239 others at Istanbul's main international airport.

"There is an attempt to turn our security forces into guilty parties, but they will not succeed in their efforts because this nation knows full well who is who," Erdogan said on Wednesday. "We will never forget our martyrs."

Turkish officials have said there are indications three suicide bombers from the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) carried out the deadly attacks at the Ataturk Airport, although no group has claimed responsibility.

Ongoing efforts

Turkish Prime Minister Binali Yildirim said efforts to identify the attackers, who arrived at the airport in taxis, were continuing.

The attackers opened fire at airport guards at the terminal entrance and a gunfight erupted before they blew themselves up one by one at around 10pm, authorities said.

Security camera footage 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.

Most of the casualties were Turkish citizens, a senior government official said.

One of the attackers "randomly opened fire" as he walked through the terminal building, shortly before three explosions, a witness told Reuters.

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"We came right to international departures and saw the man randomly shooting. He was just firing at anyone coming in front of him. He was wearing all black. His face was not masked. I was 50 metres away from him," said Paul Roos, 77, a South African tourist on his way back to Cape Town with his wife.

"We ducked behind a counter but I stood up and watched him. Two explosions went off shortly after one another. By that time he had stopped shooting," Roos said.

"He turned around and started coming towards us. He was holding his gun inside his jacket. He looked around anxiously to see if anyone was going to stop him and then went down the escalator ... We heard some more gunfire and then another explosion, and then it was over."

Ataturk Airport is one of the busiest ports in the world, serving more than 60 million passengers in 2015.

There has been a string of bombings around Turkey over the past year, some of them blamed on ISIL, others claimed by Kurdish groups.

Earlier in June, at least 11 people were killed in central Istanbul following a bombing attack targeting a police vehicle. The armed group Kurdistan Freedom Hawks, also known by its Kurdish-language acronym TAK, claimed responsibility for that attack.