"We are acting very cautiously against plots, traps and provocations that seek to drag our country into war," President Recep Tayyip Erdogan said, pledging an "appropriate and measured" response after the defence ministry said another missile was intercepted.

"Keeping our country out of this fire pit is our top priority."

The missile, which set sirens wailing at Turkey's Incirlik air base, a NATO facility where US troops are stationed near the southern city of Adana, "was neutralised by NATO air and missile defence assets," the defence ministry said.

NATO shot down a first ballistic missile from Iran on March 4, with a second intercepted on Monday.

Adana residents were woken by sirens at 3:25 am (0025 GMT), several posting footage of a fast-moving object in the sky, the Ekonomim business news website reported.

Defence news site SavunmaSanayiST said they could be "fragments of a third ballistic missile" or of the interceptor, which caught fire upon entering the atmosphere.

Iran's embassy in Ankara immediately denied any involvement, saying "no projectile" had been fired towards Turkey, but experts said it was unlikely.

"The first one you can explain it away, the second one possibly, but the third? No. This cannot be accidental," Sinan Ulgen, senior fellow with Carnegie Europe told AFP.

This leaves Ankara in a real bind," he added, saying Turkey would have to find some kind of "low-threshold way to respond".

"In a way, the Gulf countries have not responded but Turkey's political and military culture is different. It's a matter of demonstrating deterrence to Iran, so that things don't escalate further," he said.

- 'Common sense' -

Erdogan said Turkey would "maintain common sense" as it sought to respond "to the complex events around us".

Monday's incident prompted Washington to close its consulate in Adana and urge all US citizens to leave southeastern Turkey.

Incirlik is an important NATO facility used by US troops for decades. It also hosts military personnel from Spain and Poland, its website says.

Experts say it also houses 50-60 US-owned tactical nuclear weapons.

US troops are stationed at Kurecik base in Malatya where they man an early-warning radar system NATO describes as a "key element" of its missile shield that can detect Iranian missile launches.

Although Ankara has categorically denied radar data has ever been used to help Israel, its presence has rattled Tehran.

On Tuesday, Turkey said a Patriot missile defence system was being deployed in Malatya just days after NATO said it had moved to strengthen its ballistic missile defence posture.