Reports quoted police sources as saying the suspects belonged to a Turkish Sunni Islamic fundamentalist group, says David O'Byrne in Istanbul.
The Great Eastern Islamic Raiders Front is thought to have links to al-Qaeda, says our correspondent.
The consulate was moved from the centre of Istanbul to a hill on the northern outskirts of the city following the 11 September 2001 attacks in the US.
'Cowardly and dastardly'
A witness to the attack, Yavuz Erkut Yuksel, said the attackers had initially emerged from a car and surprised the police officers guarding the building.
"One of them approached a policeman while hiding his gun and shot him in the head," he told CNN-Turk.
Governor Guler said: "There is no doubt this was a terrorist attack."
The US ambassador to Turkey, Ross Wilson, said: "It is enough to say they are terrorists who carried out a cowardly and dastardly attack."
Turkish President Abdullah Gul said: "Turkey will fight to the end against those who are behind them."
Turkey has seen armed attacks from a variety of groups in recent years.
The most deadly was in November 2003, when 58 people were killed by Islamist militants in suicide bombings outside two synagogues, the British consulate and a British bank in Istanbul.
The Kurdish rebels of the PKK have also been blamed for several attacks, including a car bombing that killed six people in the city of Diyarbakir in January.
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