(Adds U.S. comment, paragraphs 9-11)

KABUL, Aug 24 (Reuters) - Three British soldiers were killed by a bomb dropped by U.S. aircraft supporting them in a battle against Taliban insurgents in southern Afghanistan, the British military said on Friday.

The incident on Thursday takes the number of British deaths in Afghanistan since the Taliban was toppled in 2001 to 73.

Two other soldiers were wounded in the incident which took place after the troops were attacked during a patrol northwest of Kajaki where U.S. contractors are reconstructing a large dam meant to bring electricity to southern Afghanistan.

"The guys were out on a routine patrol last night northwest of Kajaki," said a British military spokesman in Helmand. "They came into quite an intensive fight and during that fight they called in close air support which was provided by two U.S. F-15 aircraft."

A single bomb was dropped by the aircraft.

"We called in fire onto what in this case were the Taliban ... either the position was inaccurate or there was a problem with the bomb," the spokesman said.

Afghan officials have criticised foreign forces for killing dozens of civilians in the last two year with inaccurate air strikes.

The British Ministry of Defence said a thorough investigation would be launched.

In Washington, the U.S. State Department said it was saddened by the deaths and would also investigate the matter.

"The United States is deeply saddened by the death of three British soldiers in Afghanistan and the wounding of two others in a friendly fire incident involving ordinance dropped by a U.S. aircraft," Kurt Volker, the U.S. Principal Deputy Assistant Secretary of State for European and Eurasian Affairs, said in a written statement.

"We will investigate this tragic incident thoroughly with our British allies. We are committed to making information available as quickly as possible," he added.

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