Istanbul (CNN) In the bitter debate over where a Russian warplane was flying when Turkish aircraft shot it down, the United States took Turkey's side Monday.

The available information indicates the warplane shot down last week was in Turkish airspace, State Department spokeswoman Elizabeth Trudeau said at a Monday press briefing.

Moscow has steadfastly maintained its jet was over Syria when it was downed.

The State Department announcement came after the body of a Russian pilot who died after the jet was shot down along the Turkey-Syria border was flown back to Russia, according to Russia's Ministry of Defense.

Col. Oleg Peshkov's body arrived Monday at the Chkalovsky military airport near Moscow, according to a statement from the ministry.

Russia's state-run Sputnik news agency reported that Peshkov's body was met by Minister of Defense Sergei Shoigu and Russian air force Commander-in-Chief Victor Bondarev.

Peshkov will be buried in Lipetsk, Russia, as requested by his family, Sputnik reported.

Photos: Turkey-Syria border: Russian warplane crashes Photos: Turkey-Syria border: Russian warplane crashes A Russian warplane goes down in Syria's Bayirbucak region, near the Turkish border, on November 24, 2015. Hide Caption 1 of 6 Photos: Turkey-Syria border: Russian warplane crashes The Turkish military says it shot down the unidentified warplane, contending it repeatedly violated Turkish airspace. Hide Caption 2 of 6 Photos: Turkey-Syria border: Russian warplane crashes Turkey's semi-official Anadolu Agency cites Turkish presidential sources in reporting that a Russian SU-24 was "hit within the framework of engagement rules." Hide Caption 3 of 6 Photos: Turkey-Syria border: Russian warplane crashes The Anadolu Agency reported that a parachute was also seen leaving the jet before it crashed. The fate of the airman remains unclear. Hide Caption 4 of 6 Photos: Turkey-Syria border: Russian warplane crashes The Turkish government is strongly opposed to the Syrian regime of Bashar al-Assad. Russia, however, has backed Assad, and has had warplanes active over Syria. Hide Caption 5 of 6 Photos: Turkey-Syria border: Russian warplane crashes Heavy smoke has been seen in the area where the plane fell.

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Turkey and Russia disagree on whether the Russian plane was in Turkish airspace when it was shot down, as well as whether any warnings went out to the crew.

Russia says its planes were bombing ISIS militants in the area, though Turkish President Recep Tayyip Erdogan has said only Turkmen -- "our brothers and sisters" -- were in that region of Syria.

The incident left one pilot dead; another was rescued.

Erdogan: 'Let's talk'

After days of tough talk after the incident, Erdogan struck a more conciliatory tone Saturday, saying his government was "really saddened" by the matter and insisting he did not want to ramp up tensions.

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"We wouldn't have wished this to happen. But, unfortunately, it did," he said at an event in Balikesir.

"We hope that the tensions with Russia will not grow and result in more saddening incidents."

Erdogan appealed for dialogue, saying the U.N. climate change conference in Paris, which he and Russian President Vladimir Putin are expected to attend, would be a good place to have such talks.

"We tell Russia, 'Let's talk about this issue within its boundaries, and let's settle it,' " Erdogan said Saturday. "Let's not make others happy by escalating it to a level that would hurt all our relations."

However, his comments fell short of the apology Moscow has demanded.

Putin signs punitive decree

Putin has accused Turkey of trying to bring its relations with Russia to a "dead end," calling the incident "a stab in the back" and tying Turkey to terrorists.

JUST WATCHED Putin warns Turkey of 'serious consequences' Replay More Videos ... MUST WATCH Putin warns Turkey of 'serious consequences' 02:20

On Saturday, he signed a decree authorizing punitive economic measures against Turkey.

The decree partially suspends "visa-free" travel between the countries, mandates that Russian travel agencies stop selling tours to Turkey -- a major tourist destination for Russians -- and bans charter transportation between the nations, according to Sputnik news.

The decree also prohibits the import of certain Turkish goods and, starting next year, will prevent Russian companies from hiring Turkish citizens, Sputnik said.

The ordeal has raised questions about international leaders' ability to come together to combat ISIS, which has taken over swaths of Syria and Iraq and claimed attacks in Europe, Asia and Africa.

JUST WATCHED Turkey warns Russia not to 'play with fire' Replay More Videos ... MUST WATCH Turkey warns Russia not to 'play with fire' 01:41

French President Francois Hollande has been meeting with world leaders over the past week in an attempt to strengthen international efforts to destroy the Sunni extremist group

But the tension between Turkey -- part of the NATO alliance -- and Russia, which has been conducting its own campaign of strikes against rebel groups in Syria, would appear to complicate those efforts.