A senior official said Saudi Arabia and Kuwait were the focus of attention, but he could not rule out the other five countries on the peninsula.
CBS News Correspondent Charles Wolfson reports the State Department says it does not know anything about timing or method of attack.
"The United States government has strong indications that individuals may be planning imminent terrorist actions against U.S. interests in the Arabian Peninsula," the State Department said in a statement released Wednesday afternoon.
"In the past, such individuals have not distinguished between official and civilian targets," the statement continued, adding "we take this information seriously."
The warning followed a communications intercept, said the official, who asked not to be identified.
The warning made no direct reference to Osama bin Laden, the Saudi exile terrorist. But the official noted that the new warning is a supplement, not a replacement, for a June 22 warning in which there was a specific reference to bin Laden and the potential threat from extremist groups associated with him.
Department officials said they had no further information on specific targets, timing or method of attack.
On June 22, the State Department warned Americans in the Middle East to be especially wary of the threat of terrorism. At the time, a Marine Corps contingent in Jordan cut short its training session and returned to its sips, while the U.S. 5th Fleet sent its ships out of port in Bahrain.
The June warning followed indictments in the 1996 Khobar Towers bombing, which killed 19 Americans in Saudi Arabia.
At the time, U.S. military forces throughout the Persian Gulf were put on a heightened state of alert as a precaution.
The official was not aware if similar actions were being taken in connection with the latest threat. He noted that it was still very early in the process.
The United States has a large military presence in the Persian Gulf, including headquarters for the Navy's 5th Fleet on the island of Bahrain. A Navy carrier battle group with more than 5,000 sailors patrols the area. Also, U.S. Air Force air crews are based at Prince Sultan Air Base south of the Saudi capital of Riyadh, and U.S. Army soldiers regularly train at Camp Doha in Kuwait.
Besides Saudi Arabia and Kuwait, the other countries on the peninsula are Yemen, Qatar, Oman, Bahrain and the United Arab Emirates.
The warning will not affect the functioning of most and perhaps all U.S. embassies on the peninsula because Thursdays and Fridays are Muslim holidays, the official said.
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