The Pentagon tread cautiously Tuesday and said that it was unclear whether the Russian aircraft shot down by Turkey had, in fact, violated Turkish airspace, as the government of that nation insists.

For now, a Defense Department spokesman said that U.S. air operations over Syria will continue under the terms of the agreement that the Russians and the American-led coalition forged in October for safely sharing Syrian airspace.

"We're not going to slow down our pace and our mission continues," Pentagon spokesman Peter Cook said Tuesday.

"We do expect the Russians to abide by the [memorandum of] understanding and to do their part to make sure that the skies over Syria remain safe for our crews," Cook said. "We have the memorandum of understanding in place with the Russians that has, up to this point, proven successful in keeping our aircraft safe, our crews safe, so we don't anticipate a problem."

A Turkish F-16 jet on Tuesday fired air-to-air missiles and destroyed a Russian Su-24, forcing two Russian pilots to eject, according to both Turkish and Russian officials. Turkish officials say they fired only after repeated warnings were issued to the jet.

The incident fueled tensions across Europe and the Middle East. It remains unclear which side of the Turkey-Syrian border the Russian jet was on and the extent to which Turkey arguably was justified in shooting it down.

As to the "relative locations of aircraft and things like that, we need a little time to work all of that out. So, you've just got to give us a little time to analyze these things," said Army Col. Steve Warren, a DoD spokesman in Baghdad, said in a Tuesday briefing with reporters Tuesday.

"These things aren't as clean as they are in the movies where you're going to see where everything is," Warren said. "It's just data that has to be collected and sorted through so we know exact locations of things."

It is the first time a NATO nation has shot down a Russian jet since 1952.

Russian President Vladimir Putin denounced the incident as a "stab in the back."

The U.S. and Russia are both conducting daily airstrikes in support of opposing factions in the multi-sided civil war in Syria.

The memorandum of understanding signed Oct. 22 by the U.S. and Russia outlines procedures and rules for sharing the skies over Syria, including shared radio frequencies and safety protocols to avoid any mishaps or misunderstandings.

U.S. military officials signed the MOU on behalf of their anti-Islamic State coalition, which includes Turkey, Cook said.

The MOU applies only to Syrian airspace, Cook said, so if the Russian jet violated Turkish airspace, the MOU would not apply there.

When asked whether the Turks may have violated the agreement if the Russian aircraft was shot down inside Syrian airspace, Cook declined to comment, saying that was "hypothetical."

"We're still waiting for the details to come out exactly in this instance, but ... as the secretary has maintained, the president reiterated today, Turkey has a right to defend its airspace," Cook said.

Videos posted online showed Syrian rebels firing small arms at an ejected Russian pilot descending from the sky.

At least one of pilots is believed to be dead, which would be the first publicly disclosed Russian fatality since it began operations in Syria in September.

Turkey has repeatedly complained about Russian aircraft violating its air space during the past several months.

The U.S. recently sent six Air Force F-15Cs to Turkey's Incirlik Air Base, which the Air Force said were intended to conduct combat air patrols in Turkish airspace and to "demonstrate our resolve to defend the sovereignty of Turkish airspace."

CNN reported Tuesday that some U.S. officials believe the Russian aircraft veered into Turkish airspace for less than 30 seconds. The location of the confrontation near or over a Syrian province that is historically home to some ethnic Turks also may have fueled tension between Turkey and Russia, said James Jeffrey, a former U.S. ambassador to both Turkey and Iraq.

"So can one conclude that the overflight was deliberate? A means of warning Turkey that if it does not behave on the Syrian issue, where it is deeply at odds with Russia and [Syrian President Bashar] Assad, it might pay a high price one day? Perhaps," Jeffrey, now a fellow at the Washington Institute for Near East Policy, wrote on the institute's website Tuesday.