Group spokesman Abu Firas al-Suri said in a video posted online that the states involved had "committed a horrible act that is going to put them on the list of jihadist targets throughout the world."
The warning came as the US-led coalition widened its air strikes against the IS group in Syria and as British warplanes flew their first anti-jihadist combat missions over neighbouring Iraq.
Washington has been supported in its Syria campaign by Arab allies Bahrain, Jordan, Qatar, Saudi Arabia and the United Arab Emirates.
Seven targets were hit in Syria, the Pentagon said.
These included the border crossing into Turkey of the besieged Kurdish town of Ain al-Arab, also known as Kobane.
Muhsin al-Fadhli, a long-standing al-Qaeda operative and alleged leader of Khorasan, was killed in the strikes, according to a jihadist who fought with the group.
The United States and its coalition partners aim to destroy the Islamic State group, which controls a swathe of territory in Iraq and Syria, has murdered two US journalists and a British aid worker and is locked in a brutal war with Iraqi and Kurdish authorities.
The IS campaign has already driven 160,000 refugees into Turkey.
Washington warned that the jihadists could not be defeated in Syria by air power alone, saying that up to 15,000 "moderate" rebels would need to be trained.
President Recep Tayyip Erdogan said Turkey could take a military role in the coalition, the Hurriyet Daily reported.
It reported Erdogan saying the government would go to parliament with a motion on October 2, after which "all the necessary steps" would be taken.
Ankara had previously insisted its hands were tied because of dozens of Turkish hostages abducted by IS in Iraq but they are now free.
Washington had been reluctant to intervene in Syria but acted after the jihadists captured more territory and committed widespread atrocities, including beheading three Western hostages.
A US defence official told AFP on Friday the Syrian mission is now similar to Iraq's, with "near continuous" sorties.
Washington also plans to train and arm 5,000 Syrian rebels, although top US military officer General Martin Dempsey said 12,000-15,000 men would be required to recapture "lost territory" in Syria.
Dempsey said defeating IS would take more than air strikes and that "a ground component" was an important aspect of the campaign.
At the UN General Assembly, Russian Foreign Minister Sergei Lavrov accused Washington of declaring its "right to unilateral use of force anywhere to uphold its own interests," in a veiled reference to the Syrian campaign.
European governments have so far ruled out strikes in Syria, although Britain "reserved the right" to intervene here if there was an imminent "humanitarian catastrophe".
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