WASHINGTON, Aug 7 (Reuters) - The United States has more troops in Iraq now than at any previous time in the war, with around 162,000 members of the military in the country, the Pentagon said on Tuesday.

Pentagon spokesman Bryan Whitman said the figure was due in part to handovers between units. As part of regular rotations, new U.S. units work alongside those they are replacing for a period of time.

Whitman said that, while troop levels often fluctuated, the previous high was generally considered to be just over 161,000 in January 2005, when Iraq held national elections.

As part of a plan announced by President George W. Bush in January, the U.S. military has added some 30,000 troops to its forces in Iraq -- a measure known as the "surge".

Whitman said the regular level of U.S. forces, including troops involved in the surge, would be around 156,000 or 157,000 if no units were moving in or out.

He said the rise above 160,000 was not due to any effort to increase the surge, which is highly controversial in Washington. Democrats and some members of Bush's Republican party have argued it is time to pull troops out of Iraq.

"There is no change to the level of effort and the combat power that we are projecting into Iraq," Whitman said.

More than 3,680 U.S. troops and many tens of thousands of Iraqis have died since U.S.-led forces invaded Iraq in 2003 and toppled Saddam Hussein.

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