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He also has lauded what he describes as help that Iran provided the United States in the 2001 invasion of Afghanistan. He also has called for U.S. companies to invest in Iran, and voted against some sanctions against Tehran.

In 2009, Mr. Obama reached out to Iran, as Mr. Hagel advocated, with a video offering a new start. The offer was publicly rejected by Iran’s hard-line ruling mullahs, who intelligence officials believe are committed to building a nuclear arsenal.

The Pentagon notes as Myth 3: “Senator Hagel has been soft on Hezbollah and Hamas.”

Senator Hagel has been clear that Hezbollah and Hamas are terrorist organizations that pose a threat to Israel, the stability of the Middle East, and the United States,” the Pentagon says.

Mr. Hagel has called on Israel to negotiate with Hamas, the Palestinian militant group that governs the Gaza Strip and is dedicated to the destruction of Israel.

The Atlantic Council, a think tank of which Mr. Hagel is chairman, published a major policy document last month that puts the onus on Israel to make peace and does not mention Hamas.

The Pentagon’s myth-busting paper also rebuts the charges that Mr. Hagel “would weaken our nuclear deterrent,” “would gut the defense budget” and “lacks management experience.”

Senator Hagel has extensive government, corporate and non-profit experience that has prepared him well to be Secretary of Defense and to lead a large and complex organization,” the papers say.

A second pro-Hagel document sent to senators labeled “frequently asked questions of Chuck Hagel,” such as “Why did Hagel not sign onto a Senate-wide letter on anti-Semitism to Russian President [Boris] Yeltsin in June 1999?”

The Pentagon’s answer: “Hagel believes that America’s President is the nation’s leader and director of foreign policy and is the most effective advocate for America’s foreign policy interests.”