Gen. Martin Dempsey's plane hit by rocket at Bagram Air Field in Afghanistan

Chairman of the U.S. Joint Chiefs of Staff, Gen. Martin Dempsey (C) listens to a soldier at the International Security Assistance Force (ISAF) headquarters in Kabul, Aug. 20, 2012. Getty

Updated at 8:22 a.m. Eastern

(CBS News) LONDON - The plane of the U.S. chairman of the Joint Chiefs of Staff, Gen. Martin Dempsey, was damaged by enemy fire on the Bagram Air Field in Afghanistan, causing minor damage to the C-17 plane and leaving two American members of the ground crew with minor injuries from shrapnel, according to U.S. officials.

The plane was empty on the tarmac at Bagram when an unspecified projectile struck nearby overnight, and Dempsey's trip to Afghanistan was not affected, according to the Pentagon. The top U.S. military officer was safe in his quarters when the incident occurred.

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Dempsey left Afghanistan Tuesday morning on a different plane due to the damage to his C-17 from shrapnel, according the the International Security Assistance Force - Afghanistan, or ISAF.

A military helicopter was also damaged in the overnight attack on Bagram.

Taliban spokesman Zabihullah Mujahid claimed responsibility for the two rounds of artillery fired on the air base. His claim could not be independently verified.

The sprawling U.S.-controlled airbase regularly comes under rocket or mortar fire from outside of its perimeters - approximately twice per month, according to ISAF - but the attacks rarely inflict significant damage.

The Joint Chiefs chairman arrived in Afghanistan Monday on an unannounced visit to meet with his top commanders in the country, as well as senior Afghan military and civilian officials.

His visit came amid a worrying spike in so-called "insider attacks" on U.S. and other international forces, whereby Afghan security forces turn their guns on the Western forces working alongside them.

  • Tucker Reals

    Tucker Reals is the CBSNews.com foreign editor, based at the CBS News London bureau.

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