One of the sites, called the Incirlik air base, is where some US nuclear warheads are kept. The other is the Kurecik radar station.
President Recep Tayyip Erdogan spoke in response to a threat of American sanctions over Ankara’s military offensive in Syria targeting US-backed Kurdish forces.
His comments also followed a US senate resolution over Armenian claims about mass killings a century ago – a move which has further increased tensions between Ankara and Washington.
The resolution last Thursday recognised the Armenian deaths in eastern Anatolia in 1915 were genocide.
Turkey has rejected this claim as it denied the killings were systematically orchestrated.
In a TV interview, Mr Erdogan said: “The US Senate’s decision on the so-called Armenian genocide is null and void for Turkey.
“In the case of sanctions, we can take steps to close Incirlik and Kurecik. If the United States continues to act like this, we have steps to take as well.”
He said of possibly shutting Incirlik: “If it is necessary for us to take such a step, of course we have the authority.
“If this is necessary, together with our delegations, we will close down Incirlik if necessary.”
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He added Turkey could also close down the Kurecik radar base.
He said: “If they are threatening us with the implementation of these sanctions, of course we will be retaliating.”
Mr Erdogan said the US bill was “completely political”, adding: “It is very important for both sides that the US does not take irreparable steps in our relations.
“We regret that the polarisation in US domestic politics has had negative consequences for us and that some groups abuse developments about our country for their own interests in order to weaken [President] Trump.”
Mr Erdogan also suggested Turkey could respond with parliamentary resolutions recognising the killings of indigenous Americans in past centuries as genocide.
Turkey said its military offensive this year was aimed at creating a “safe zone” for Syrian refugees and to keep it free from Kurdish fighters it views as terrorists.
The Incirlik air base, located about 100 miles from Turkey’s border with Syria, is often referred to as one of the major strategically located US military bases.
The Kurecik radar station hosts NATO’s early-warning radar systems against ballistic missile attacks.
