The statement appeared on an Islamist Web site known for posting messages from militants, including the video in which a terror group with al Qaeda links executed the American kidnapped in Iraq, .
The authenticity of the statement, signed "Al Qaeda on the Arabian Peninsula," could not be confirmed.
CBS News Correspondent Bob Orr reports the Department of Homeland Security said Monday that there is near constant chatter on Islamic Web sites about al Qaeda's interest in attacking U.S. and Western interests in Saudi Arabia. But, the department says, there is no indication at this time that al Qaeda is targeting airlines inside the U.S.
In Washington, State Department deputy spokesman Adam Ereli noted that existing U.S. travel warnings call attention to possible threats to commercial aviation in Saudi Arabia and urge Americans to take that into account when making their travel plans.
The statement referred to "crusaders" and warned that "all that is affiliated with these crusaders - from compounds, bases and means of transport, especially Western and American airlines – will be the direct targets of our next operations in the path of holy war which, with God's help, we will not be diverted from, especially in the near future."
The statement begins by warning all Muslims to avoid "contact with the American and Western crusaders and all non-believers in the Arabian peninsula."
It urges Muslims to stay away from Americans and Westerners "in their homes, compounds, movements and means of transport - in all shapes and forms."
The statement said the warning aimed to spare Muslim blood. "We act only to protect them, their religion, honor and life," the statement said.
Militants have stepped up attacks on foreigners in Saudi Arabia in past weeks, most recently in a shooting Sunday that killed an Irish cameraman and wounded a British Broadcasting Corp. reporter.
On May 29, gunmen attacked a complex housing oil workers in the eastern city of Khobar, killing 22 people, most of them foreigners. During that assault - claimed by al Qaeda - the gunmen reportedly separated out and spared Muslims and Arabs and killed non-Muslims.
Previous bombings by al Qaeda that killed Muslims raised an outcry in Saudi Arabia against the terror network.
The statement called on "all security personnel, guards of crusader compounds and American bases, and all those that have stood by America and its allies ... to return to the right path, to separate themselves from non-believers, to become their enemies and to fight holy war against them by money, word and weapon."
"This enemy must be fought," the statement said. "There is no other way but to fight it and eradicate it."
The statement appeared to be concerned with the American presence in Saudi Arabia rather than in Iraq. It referred to the Arabian Peninsula in its signature and it spoke of "agents of the tyrannical Saudi government."
The Web site has carried several statements and claims of responsibility from Islamic militants, most recently for the Khobar attack.
During the coming months, a number of high-profile events in the United States could make tempting targets, starting with this week's at Sea Island, Ga. Later in the summer, the Democrats and Republicans each hold their national conventions.
Overseas, two major sports gatherings — the European soccer championships in Portugal and the Olympics in Greece — are also potential targets.