UN leader Ban Ki-moon expressed his 'deep concern' over the plane incident in a telephone conversation with Turkey's foreign minister.
President Bashar al-Assad meanwhile formed a new cabinet, but kept the key posts unchanged.
NATO member Ankara acknowledged that one of its warplanes may have violated Syrian airspace after Damascus confirmed shooting down the F-4 Phantom on Friday. Its muted response however was seen as a bid to take the tension out of the latest rift between the former allies.
A Syrian military spokesman told the official SANA news agency early Saturday that they had shot down what had at the time been an unidentified object coming in low and fast over its territorial waters.
Anti-aircraft batteries hit the plane about a kilometre from the coast and it crashed some 10 kilometres off Latakia province, he added.
Turkish President Abdullah Gul said it was not unusual for warplanes flying at high speed to cross maritime borders, but stressed that such actions were not “ill-intentioned.”
Naval forces from both nations were searching for the two missing crew.
Turkey’s Deputy Prime Minister Bulent Arinc played down the tensions.
“We should be calm … Yes, we accept this is a critical matter but we don’t have clear information,” he told Anatolia news agency.
The results of an ongoing investigation would be publicised “as soon as possible.”
UN leader Ban Ki-moon had expressed his “deep concern” over the incident in a telephone conversation with Turkey’s foreign minister, a spokesman said.
“He commended Turkey for the restraint shown in its initial reaction,” said the UN spokesman, Martin Nesirky.
“The secretary general urged both to continue to address the situation diplomatically,” he added.
The Syrian Observatory for Human Rights said 116 people, 77 of them civilians, were killed in violence across the country on Saturday as regime forces stepped up attacks on towns.
The Britain-based monitoring group said the civilians had been killed in the bombardment of rebel bastions.
They included a family of six in Deir Ezzor, eastern Syria; a man and his three children in Kfaraaya, in the central province of Homs; and four members of the same family, including two children, in Hama, central Syria.
Nineteen soldiers were killed in fighting with rebels, and 10 died among the rebel forces, the Observatory said. Another 10 soldiers were gunned down as they tried to defect to anti-regime forces, it added.
On Friday, at least 116 people were also reported killed.
The International Committee of the Red Cross condemned the killing of a Syrian Arab Red Crescent volunteer, in the fourth such incident in the country’s deadly unrest.
Bashar al-Youssef, 23, was shot and fatally wounded on Friday in Deir Ezzor in eastern Syria, the two organisations said in a joint statement.
“This comes at a time when the ICRC and the Syrian Arab Red Crescent are virtually the only organisations able to work in areas affected by the violence in Syria,” said Alexandre Equey, deputy head of the ICRC’s delegation there.
Assad meanwhile announced the formation of a new government under Prime Minister Dr Riad Hijab, less than two months after controversial parliamentary elections boycotted by the opposition.
But he left his key ministers in place: Foreign Minister Walid al-Muallem, along with the defence and interior ministers, Daoud Rajha and Mohammad al-Shaar.
Rajha, in the post since August, was among those sanctioned by the United States for his role in the deadly crackdown on Syrian protesters.
Abdel Basset Sayda, head of the main opposition Syrian National Council, dismissed the new line-up as a sham designed “to give the impression that reforms have been brought in.”
With the key posts unchanged, there was “no real change,” he said.
The new cabinet assumes power amid an intensification of repression and clashes, which last week led to the halt of the United Nations observer mission.
Britain’s Guardian newspaper, meanwhile, reported that Saudi Arabia was set to pay the salaries of the rebel Free Syrian Army to encourage mass defections from Syria’s army. Some of the rebel fighters are defectors from Syria’s army and are based in Turkey.
Turkey-Syria relations have already been strained by Erdogan’s outspoken condemnation of the Assad’s government’s bloody crackdown, which rights activists say has killed more than 15,000 people since March 2011.
A Russian ship carrying a controversial cargo of Mi-25 attack helicopters that Moscow had repaired for Syria returned to Russian waters Saturday.
But Interfax has reported that the ship will set off again on its voyage to the Syrian port of Tartus, this time accompanied by at least one other Russian ship.
The Alaed was forced to return from its journey to Syria after its mission was revealed by the US State Department, prompting its British insurers to withdraw coverage.