Updated

The State Department was warning American citizens in even more countries Thursday to be on alert as anti-U.S. protests spread to Oman and showed no signs of stopping there.

The Department of Homeland Security and the FBI also issued a joint intelligence bulletin warning that the violent outrage aimed at U.S. embassies could be spread to America by extremist groups.

In a statement to Fox News, a DHS official said that there is no specific, credible information at this time to indicate that the attacks have increased the threat of violent reaction in the U.S., but it will continue to identify potential threats and take appropriate measures.

The State Department's Twitter account said late Thursday that "demonstrations have begun" in front of the U.S. Embassy in the city of Muscat, Oman. Citizens should "exercise caution," the department said.

The same account warned about possible protests near the U.S. embassies in Kuwait and Jordan.

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    For Jordan, the department warned about "possible demonstrations" Thursday evening and going into Friday. For Kuwait, the department cited "possible protests "in front of the compound "over the next few days" starting Thursday night.

    The warnings marked the latest developments in the demonstrations, which earlier spread to the Yemeni capital of Sanaa and continued into their third day outside the U.S. Embassy in Cairo, Egypt.

    Four Americans were killed in an attack on the U.S. Consulate in Benghazi, Libya, on Tuesday.