Three of the suspects were detained in Istanbul, while the fourth was apprehended in another city. All were Turkish nationals, Atalay said.
Police have been looking for the driver of the car in which the three attackers drove to the consulate building. It is unknown whether he was among the four detained.
The US ambassador to Turkey has called the attack an obvious act of terrorism, while CNN Turk televsion on Wednesday quoted police sources as saying al-Qaeda was behind the attack.
The interior minister said investigators were trying to establish whether the assailants belonged to any outlawed group, denying reports that one of them had spent time at the US detention centre at Guantanamo Bay, Cuba.
Hoda Abdel-Hamid, Al Jazeera's correspondent in Istanbul, said: "There are several [local news] reports that say that three of the attackers were Turkish nationals and ... have been to Afghanistan at some point. One of them [may be from] south east Turkey.
The Radikal newspaper said Erkan Kargin, one of the attackers killed in the shootout, crossed into Iran in September 2006 and returned to Turkey eight months later. Iran does not require visas for Turkish citizens and fighters reportedly travel to Afghanistan through Iran.
NTV television reported that Kargin is thought to have undergone military training in Afghanistan.
The US said it was unable to confirm or deny reports of al-Qaeda involvement.
Sean McCormack, a state department spokesman, said: "I can't say either way. I can't refute them. I can't support them at this point. In terms of our view, it's too early to tell in the investigation."
He said Washington was working closely with the Turkish government "to
determine who is responsible for it and, of course, as best we can, hold to account anybody who was involved" in its planning and execution.
No one has yet claimed responsibility for the attack.
Speaking to Al Jazeera, Osman Faruk Logoglu, the former Turkish ambassador to the US, said: "I think it is impossible to say [who was responsible]. What we can say is that this is a terrorist act pure and simple.
"In terms of reasons... there are speculations of all sorts, one line of thinking is that this is a message to the US and their policies in the region. The other suggestion is that it is the PKK [Kurdish Workers' Party].
"What they have revealed to us so far is that they somehow trained in Afghanistan and this leaves a lot of people to jump to the conclusion that there is an al-Qaeda connection," he said.