"If you can kill a disbelieving American or European - especially the spiteful and filthy French - or an Australian, or a Canadian or any other disbeliever... Including the citizens of the countries that entered into a coalition against the Islamic State, then rely upon Allah, and kill him," said Abu Mohammed al-Adnani, the group's spokesman.
"Kill the disbeliever whether he is civilian or military," he said in the message, which was released in multiple languages.
US Secretary of State John Kerry said that more than 50 countries have come forward with commitments as part of the coalition, including Egypt and other Arab states.
The jihadist group, which has declared a "caliphate" straddling Iraq and Syria, controls swathes of territory in both countries.
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IS has executed hundreds of Iraqis and Syrians, as well as foreign hostages, and its brutal campaign has forced more than a million people from their homes.
The hundreds of foreigners from various Western countries fighting alongside IS have sparked fears that they could return home to carry out attacks.
Today, Australian Prime Minister Tony Abbott warned that any of its citizens "who fight with terrorist groups... Will be arrested, prosecuted and jailed for a very long time."
Adnani praised militants in Egypt's Sinai Peninsula, calling on them to "cut the throats" of those fighting for President Abdel Fattah al-Sisi and saying Tunisians should follow their example.
And he called on Muslims in Libya to unite, saying that "your division is from Satan."
"We are in a new era, an era where the (Islamic) State, its soldiers, and its sons are leaders, not slaves," Adnani said.
"We will conquer your Rome, break your crosses, and enslave your women, by the permission of Allah, the Exalted."
He also mocked the US air campaign, saying that "the battle cannot be decided from the air".