Davutoglu told Turkey's TRT television that, "according to our conclusions, our plane was shot down in international airspace, 13 nautical miles from Syria."
Damascus did not issue a warning before shooting down the plane, which was on an unarmed training mission to carry out a radar system test, Turkey said.
"The Syrians knew full well that it was a Turkish military plane and the nature of its mission," he said. "Nobody should dare put Turkey's (military) capabilities to the test."
US Secretary of State Hillary Clinton lashed out at Syria for the "brazen and unacceptable" downing of the Turkish jet and vowed to work with Ankara on a suitable response.
"It is yet another reflection of the Syrian authorities' callous disregard for international norms, human life, and peace and security," Clinton said in a statement.
British Foreign Secretary William Hague said President Bashar al-Assad's regime "should not make the mistake of believing that it can act with impunity. It will be held to account for its behaviour."
Italy, another NATO member, also condemned the regime for the shooting incident. "This is ... extremely serious and unacceptable," Foreign Minister Giulio Terzi said.
He added that Rome voiced its "strong indignation and condemnation" and that Italy would "actively participate" in the NATO meeting, which is to be held on Tuesday.
A NATO spokeswoman said that, "under Article 4, any ally can request consultations whenever, in the opinion of any of them, their territorial integrity, political independence or security is threatened."
Damascus said it downed the F-4 Phantom on Friday after it violated Syrian airspace.
"Syria was merely exercising its right and sovereign duty and defence," Syrian foreign ministry spokesman Jihad Makdissi was quoted as saying on Sunday in Al-Watan, a pro-government daily.
"There is no enmity between Syria and Turkey, but political tension (exists) between the two countries.
"What happened was an accident and not an assault as some like to say, because the plane was shot while it was in Syrian airspace and flew over Syrian territorial waters," Makdissi said.
Turkey acknowledged on Saturday that the plane may have done so, in comments seen as a bid to cool tensions between the former allies, but it now appears to have taken a harder stance.
CNN-Turk television reported that search and rescue teams have located the wreckage of the jet at a depth of 1,300 metres (4,265 feet) in the sea, but did not give its precise location or refer to the fate of the two missing pilots.
Ankara said it could not confirm the report.
"We will bring this affair before public opinion and international law in the name of Turkey's honour," Davutoglu said.
Turkish-Syrian relations have already been strained by Prime Minister Recep Tayyip Erdogan's outspoken condemnation of the Assad's regime's bloody crackdown, which rights activists say has killed more than 15,000 people since March 2011.
UN chief Ban Ki-moon expressed his "deep concern" about the incident, particularly about the "potential serious implications" for the region, spokesman Martin Nesirky said.
In a telephone call with Davutoglu, the UN chief "commended Turkey for the restraint shown in its initial reaction and appreciated Turkey and Syria for conducting a joint search operation."
-- Bad week for Assad --
The Syrian Observatory for Human Rights said 76 people were killed on Sunday in Syria, including 39 civilians, 27 soldiers and 10 rebels.
The Observatory reported that following an attack on an artillery battalion in Aleppo, a number of soldiers defected, taking with them a large quantity of weapons.
The official SANA news agency reported that regime troops "were engaged in combat against a terrorist group that attacked people in the Jabaliye neighbourhood of Deir Ezzor killing scores of terrorists."
Syrian government uses the term "terrorists" to describe the rebels.
In another setback for the regime, rebels captured 11 government soldiers in the central province of Damascus, it added.
"This is one of the bloodiest weeks in the conflict," Rami Abdel Rahman, head of the Observatory, said.
The Observatory also reported that rebels had shot down a Syrian regime helicopter near the Jordanian border.
According to Observatory figures, 94 people were killed in Syria last Monday, 62 on Tuesday, 88 on Wednesday, 168 on Thursday, 116 on Friday and 116 more on Saturday.
"It's like we are in a war," Abdel Rahman said. "Sometimes when two countries are at war, not even 20 people are killed a day. But now in Syria it has become normal to have 100 killed each day."
A Russian ship that tried to deliver attack helicopters to Syria entered the northern port of Murmansk on Sunday after being forced to turn back when news of its mission was leaked.
An unnamed Russian diplomat said the ship, the Alaed, would soon try again to make the highly controversial delivery under the Russian flag.
The switch appears to be an attempt to avoid security inspections that come when sailing under the flag of a third country.
The Alaed was forced to turn back after its mission was initially mentioned by the US State Department and then reported in the British press. Those reports prompted the ship's British insurer to withdraw coverage.