The US military has begun an investigation after it emerged that a course at one of the country's leading military academies was teaching that Islam was an enemy of America.

The voluntary course, attended by officers at the Joint Forces College in Virginia, ran for a year before it was stopped last month after a student complained.

The officer in charge of the course has been suspended from teaching, but remains in his job.

During the course it was also suggested that the US might ultimately have to obliterate the Islamic holy cities of Mecca and Medina without regard for civilian deaths, following World War II precedents of the nuclear attack on Hiroshima or the allied firebombing of Dresden.

"They hate everything you stand for and will never coexist with you, unless you submit," the instructor, Army Lieutenant Colonel Matthew Dooley, said in a presentation for the course last July.

The college for professional military members teaches mid-level officers and government civilians subjects related to planning and executing war.

Lt Col Dooley also presumed, for the purposes of his theoretical war plan, that the Geneva Conventions that set standards of armed conflict are "no longer relevant."

The course on Islam was an elective taught since 2004 and not part of the required core curriculum.

Within days of suspending the course, Joint Chiefs Chairman General Martin Dempsey ordered all service branches to review their training to ensure other courses do not use anti-Islamic material.

Gen Dempsey said the material in the Norfolk course was counter to US "appreciation for religious freedom and cultural awareness."

"It was just totally objectionable, against our values, and it wasn't academically sound," he said when asked about the matter at a Pentagon news conference.

"This wasn't about ... pushing back on liberal thought; this was objectionable, academically irresponsible."

A six-month review the FBI launched into agent training material last September uncovered 876 offensive or inaccurate pages that had been used in 392 presentations, including a PowerPoint slide that said the bureau can sometimes bend or suspend the law in counterterror investigations.