"The order will provide the commander-in-chief additional flexibility should military options be required to protect American lives, citizens and interests in Iraq," Rear Admiral John Kirby, the Pentagon spokesman, said.
Ordered by Defense Secretary Chuck Hagel, the move comes amid calls for air strikes to blunt a lightning offensive by Sunni Islamic militants that threatens Baghdad and the country's Shiite-led government.
US President Barack Obama said Friday the United States would not send in US ground troops but that he was weighing all other options.
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The Bush is being accompanied by two other warships -- the guided-missile cruiser USS Philippine Sea and the guided-missile destroyer USS Truxtun, Kirby said in a statement.
The carrier's movement into the Gulf from the north Arabian Sea was expected to be completed by the end of the day, he said.
"American naval presence in the Arabian Gulf continues to support our longstanding commitments to the security and stability of the region," he added.