BAGHDAD—Australia has suspended air operations in Syria amid escalating tensions between Washington and Moscow after Russia threatened to track American and coalition aircraft in the war-torn country as targets.

“As a precautionary measure, Australian Defense Force strike operations into Syria have temporarily ceased,” a statement from the Defense Ministry said Tuesday.

The American ally’s decision to back out of U.S.-led coalition airstrikes in Syria comes hours after the U.S. shifted some of its own flight patterns in the country to minimize risks, following Russia’s warning on Monday that it would use air defense systems or Russian pilots to track flights west of the Euphrates.

The current tensions between the U.S. and Russia, which back opposite sides in the Syrian conflict but are also fighting Islamic State in the country, began Sunday when an American jet fighter shot down a Syrian regime warplane after it targeted U.S.-backed Syrian fighters who were leading the assault on Islamic State’s de facto capital, Raqqa.

Russia, allied with the Syrian regime of Bashar al-Assad, responded to the U.S. strike with threats to cut official lines of communication that are meant to prevent midair mishaps and to treat U.S.-led coalition planes as “targets.” It, however, stopped short of threatening to shoot them down, giving some U.S. officials hope that the situation won’t worsen.