"The Russian Federation will be responsible for any undesired incident that may occur," the ministry warned.
The incident occurred Saturday in the Yayladagi region of Turkey's southern Hatay province.
"The Russian aircraft exited Turkish airspace into Syria after it was intercepted by two F-16s from the Turkish air force, which were conducting patrols in the region."
A spokesman for Russia's defense ministry dismissed any idea that the incident was anything nefarious, stating flight patterns that change "under certain weather conditions" might help explain what happened.
"This current incident is a result of bad weather conditions in this region," spokesman Igor Konashenkov told reporters. "You shouldn't look for conspiracy theories."
Turkey, Russia at odds over Syria policy
Turkish Prime Minister Ahmet Davutoglu said Monday the violation was "a mistake," according to the semiofficial Anadolu news agency.
"Our foreign minister called the Russian foreign minister and said clearly that this should not be repeated," Anadolu quoted Davutoglu as saying in an interview with Haberturk TV. "The information from Russia this morning was that this happened by mistake and that they respect Turkish borders and that it will not be repeated.
"Whoever violates our airspace, our rules of engagement are clear," he said. "We will warn whoever violates our borders and our airspace in a friendly manner. This country can be whichever and Russia is our neighbor, our friend. In this way, there is no tension between Turkey and Russia. The Syria issue is not a Turkish-Russian crisis," he said.
NATO's North Atlantic Council issued a statement Monday on what it called "the recent dangerous military activities of the Russian Federation in and around Syria," saying there were violations of Turkish airspace by Russian Su-30 and Su-24 aircraft both Saturday and Sunday.
"Turkish fighter aircraft responded to these incursions by closing to identify the intruder, after which the Russian planes departed Turkish airspace," the statement said.
Turkey and Russia are at odds regarding Syria's civil war.
Ankara's position is that Syrian President Bashar al-Assad has to go for the conflict to end. Moscow backs the Syrian leader and has begun airstrikes that it says are against ISIS militants.
NATO Secretary General Jens Stoltenberg said the airspace violation was "unacceptable."
Stoltenberg said he met Turkish Foreign Minister Feridun Sinirlioglu on Monday to discuss Russia's moves.
"Russia's actions are not contributing to the security and stability of the region," he said in a statement.
"I call on Russia to fully respect NATO airspace and to avoid escalating tensions with the Alliance."
A report from the Russian state news agency Sputnik
accused the United States specifically of making "a fuss" about what it called an "accidental incursion into Turkish airspace."
"Moscow told Ankara that the Russian pilot that violated Turkish airspace was mistaken and that it would not happen again," the Sputnik report stated.
Russian airstrikes continue in Syria
Moscow announced over the weekend
it was intensifying the airstrikes, which started Wednesday.
Over the last 24 hours, Russian Su-34, Su-24M and Su-25 planes hit nine ISIS targets in Syria, Russia's Defense Ministry said Monday.
It said the air force had used "pinpoint strikes" against ISIS facilities in Hama, Homs, Idlib and Latakia provinces.
Targets destroyed included an ISIS command center, communications center, training camp and ammunition depots as well as artillery weapons and vehicles, the ministry said.
Meanwhile, the U.S.-backed coalition against ISIS, Operation Inherent Resolve, said its forces continued to attack ISIS in Syria and Iraq on Sunday. The coalition includes the United States, Britain, Turkey, France, Germany, Qatar and Saudi Arabia.
"In Syria, coalition military forces conducted eight strikes using bomber and remotely piloted aircraft. Separately in Iraq, coalition military forces conducted 13 strikes coordinated with and in support of the Government of Iraq using fighter, fighter-attack, and remotely piloted aircraft against ISIL targets," it said in a statement, referring to ISIS by another name.
Targets included militant positions, tactical units, weapons caches and vehicles, it said.
Since 2011, Syria has been torn apart by a brutal civil war that has seen the rise of extremist groups including ISIS. Moscow says its strikes are targeting ISIS, al-Nusra Front and "other terrorist groups" in Syria.
But the U.S-backed coalition against ISIS accuses Russia of attacking civilians and Syrian groups opposing al-Assad.
Russian Foreign Minister Sergey Lavrov told reporters Monday in Moscow that Russian and U.S. officials had engaged in high-level discussions about Russia's actions in the Middle Eastern country.
"Our presidents discussed it, I discussed it with Secretary (John) Kerry," Lavrov said, adding that the Pentagon and the Russian Defense Ministry also held a video conference. "Both sides agreed to cooperate to avoid unintended incidents."
Lavrov said Russia had asked the United States for more military contacts and expected to receive a response within the coming days.
Russia's state-run news agency Sputnik reported
that Lavrov had asked for contacts within the opposition Free Syrian Army -- which the United States backs -- saying Moscow would be willing to work with it to end the crisis.
Lavrov described the Free Syrian Army as a "phantom group" about which little was known, Russia's state-run Tass news agency reported.
"No one has told us where the Free Syrian Army operates or where and how the other units of the moderate opposition act," Tass quoted him as saying. "We will even be ready to establish contact with it, if these are indeed efficient armed groups of the patriotic opposition that consist of Syrians."