One of the two pilots was killed in the air by fire from the ground, according to Russia's state-run news agency RIA Novosti. The fate of the second pilot wasn't disclosed.
Meanwhile, a Russian marine was killed on Tuesday during an operation to rescue the two pilots, who were flying an Su-24 warplane in a combat sortie, according to RIA Novosti.
Turkey and Russia exchanged bellicose language after the downing of the plane, raising fears in the international community that the Syrian conflict could spiral into something wider.
The Russian plane was dealt with because it "did not answer our warning," Turkish President Recep Tayyip Erdogan said Tuesday.
ISIS isn't present at that border area, but Turkmen were there, Erdogan said. Anyone who bombs that area attacks "our brothers and sisters -- Turkmen," Erdogan said in Ankara. Turkmen are a Turkic-speaking, traditionally nomadic people who live primarily in Central Asia, but a small minority of them can be found in the Middle East, primarily in northern Iraq, Iran and Turkey.
Erdogan said the plane incident was not something Turkey wanted to see happen, and "this does not indicate any animosity" toward any country.
He added the downed jet was "one of two" planes but didn't elaborate beyond that.
It's been Turkey's cool approach that has prevented similar incidents up to now, he added.
Turkey's ambassador to the United States, Serdar Kilic, tweeted: "Understand this: Turkey is a country whose warnings should be taken seriously and listened to. Don't test Turkey's patience. Try to win its friendship."
A U.S. official told CNN that a calculation shows the Russian jet was in Turkish airspace for 30 seconds or less. The Turkish government has said that it issued 10 warnings over five minutes but did not say all of those warnings occurred while the jet was in their airspace.
Russian President Vladimir Putin said the downing of the plane would have "serious consequences for Russia's relationship with Turkey."
The shooting of the plane, Putin said, "represents a stab in the back by the terrorists' accomplices. I can't describe what has happened today in any other way. Our plane was downed over Syrian territory by an air-to-air missile from a Turkish F-16 jet.
"The plane fell on Syrian territory 4 kilometers (2.5 miles) away from the Turkish border. It was flying 1 kilometer away from the Turkish border when it was attacked. In any case, neither our pilots nor our jet posed any threat to Turkey. That is obvious. They were carrying out an operation fighting against ISIL in Northern Latakia." (ISIL is another acronym for ISIS.)
The two Russian pilots managed to eject their Su-24 plane, the Russian military said.
Two Russian Mi-8 helicopters performed a search-and-rescue operation, but one of them was damaged by small arms fire and made an emergency landing, Russian Lt. Gen. Sergei Rudskoy said.
One Russian marine was killed.
"The helicopter was destroyed by mortar fire conducted from the territory controlled by illegal, armed groups," Rudskoy said.
Future Russia airstrikes "will be carried out only under cover of fighter aircraft," Rudskoy said.
Also, the Russian cruiser Moskva will go to the shore zone of Syrian port of Latakia, and the military "warns that all the potentially dangerous targets will be destroyed," Rudskoy said.
New video published on social media by a Syrian rebel group allegedly shows Turkmen rebels shooting at the two ejected pilots landing on the border between Turkey and Syria.
CNN couldn't immediately confirm the video's claim.
Speaking in Turkish language, a man shouts off-camera, "don't shoot at them" and "capture them alive," referring to the two Russian pilots.
Heavy gunfire can be heard on the video. The rebels also shout, "God is great!"
Erdogan on Tuesday pointed how Turkey has been hosting 2 million Syrian refugees while European countries have panicked over smaller numbers seeking refuge there.
It's not possible to resolve terrorism or refugee problems without finding a sustainable solution to Syria, but the Syrian regime of President Bashar al-Assad and countries that support it have started a new assault that does not fit with finding a resolution for the area, Erdogan said.
Turkey vehemently opposes the Assad regime. Russia is backing it.
NATO calls emergency meeting
After holding an emergency meeting in Brussels on Tuesday, NATO's governing body, the North Atlantic Council, said Turkey informed the body about the plane's downing.
Turkey is a member of NATO, which considers an attack on one of its members to be an attack on them all.
NATO Secretary General Jens Stoltenberg urged "calm and de-escalation" to resolve the Turkey-Russia situation, but he noted how Russian forces approach allies' borders.
"I have previously expressed my concern about the implications of the military actions of the Russian Federation close to NATO's borders," the Stoltenberg said. "This highlights the importance of having and respecting arrangements to avoid such incidents in the future.
"As we have repeatedly made clear, we stand in solidarity with Turkey and support the territorial integrity of our NATO ally, Turkey," he added.
NATO continues to follow the matter, Stoltenberg said.
A NATO official told CNN that "when Russian jets violated Turkish airspace a few weeks ago, the Council did meet in an extraordinary session, which resulted in a condemnation of the incursion."
Not long after the plane was shot down Tuesday morning, spitting fire and diving nose-first toward the ground, Turkey took responsibility. Turkey's semiofficial outlet, the Anadolu Agency, quoted Turkish presidential sources as saying the Russian Su-24 was "hit within the framework of engagement rules" in Syria's Bayirbucak area, near the border with Turkey.
Russian officials denied the plane had violated Turkish airspace.
While ISIS does not operate in the area where the plane went down, other rebel groups do, including al Nusra Front -- al Qaeda's affiliate in Syria -- along with more moderate U.S.-backed groups.
Abu Ibrahim al-Sheghri, the military leader in the 10th coastal brigade and part of the Turkmen Mountain Military Operation Room, told CNN that the body of one of the pilots had been found in the Nibh Almur area of Syria. The brigade is searching for the other pilot in the same area, he said.
Early this year, Moath al-Kasasbeh, a Jordanian pilot whose plane crashed in Syria the previous December, was burned alive
by ISIS while he was trapped in a cage.
U.S. and French Presidents comment
U.S. President Barack Obama said Tuesday that "Turkey has the right to defend its country and its airspace," but he acknowledged that U.S. officials "don't have all the information yet."
Obama said it was important that Russia and Turkey are in contact with one another to "take measures to discourage any kind of escalation."
He said the plane incident "points to an ongoing problem with the Russian operations" in Syria, which are taking place very close to the Turkish border. Russia has been going after "moderate opposition" that has the support of Turkey, Obama said.
If Russia instead focused on fighting only ISIS, "some of those conflicts or potential for escalation are less likely to occur," Obama said.
He said the encounter also "underscores the importance of our moving the political track along as quickly as possible" when it comes to resolving the Syrian civil war.
Obama made his remarks at a news conference with French President Francois Hollande at the White House, held to discuss the recent terror attacks on Paris.
Hollande called the plane incident "a serious one" and said Turkey is providing information to NATO "so that we can find what really happened."
"We must prevent any escalation," Hollande said.
Hollande will be traveling to Russia this week to meet with Putin and discuss taking action against ISIS.
"We must find a solution to the Syrian crisis," Hollande said.
A brutal civil war
Turkey released a purported image of the flight path of the plane showing it had violated Turkish airspace. Two Turkish F-16s responded "within engagement rules," the country's officials said.
But the Russian Defense Ministry said "objective monitoring confirmed" the plane was not in Turkish airspace.
"The Su-24 bomber jet was in Syrian airspace at the altitude 6,000 meters, the Russian Defense Ministry said," according to Sputnik. "The pilots were reportedly able to parachute out of the jet before it crashed."
Syria has been embroiled for more than four years in a civil war that has killed hundreds of thousands of people, sent millions of families fleeing and laid waste to cities.
Skirmishes between Turks and Syrians have taken place in the past, with Turkish officials accusing Syrian planes of violating Turkish air space.
Sajjan Gohel, international security director for the Asia-Pacific Foundation, a think tank, described the downing of the plane as "a very significant escalation."
"It's very much the last thing that's needed right now, especially in the aftermath of the Paris attacks, when there was hope that Russia could form an alliance with France and with the United States against ISIS," Gohel said. "This is going to complicate things. This is going to add unnecessary tensions that really weren't required at this critical juncture."
He said the downing of the Russian plane would hamper efforts to form a united front against ISIS.
"This is a situation that unfortunately was almost inevitable at some point, because Turkey has long been accusing Russia of interfering in their airspace," Gohel said. "They've threatened them in the past. And even though economic relations between the two countries are strong -- politically, there have been tensions recently."
Syria's internal conflict has become a massive proxy war for numerous international powers, both in the region and outside it -- a situation that has added to the perception that incidents such as Tuesday's plane downing were inevitable.
Currently, the United States, Russia, France, Australia, the Gulf states, Turkey, Israel, Iran, Jordan and Hezbollah are involved, one way or another, in military activity in Syria.
In March 2014, Turkey shot down a Syrian fighter jet
after the warplane strayed into its airspace, according to Erdogan, the current president, who was prime minister at the time.
"Our F-16s went up in the air and shot that plane down. Why? Because if you violate my airspace, then from now on, our slap will be hard," Erdogan told supporters at a campaign rally in 2014.
But state-run media in Syria called it an act of "blatant aggression" and said the downed plane was over northern Syria at the time.