(Adds White House comment, details)

By Kristin Roberts

WASHINGTON, Aug 15 (Reuters) - Donald Rumsfeld, architect of the unpopular Iraq war, resigned as defense secretary before last year's November election but his decision was not announced until after the voting, according to his resignation letter obtained by Reuters on Wednesday.

The letter was dated Nov. 6, the day before voters, angered by Iraq, went to the polls and swept President George W. Bush's Republicans from power in Congress. According to a stamp on the letter, Bush saw it on election day.

The president, however, did not announce that Rumsfeld would leave until the day after the election.

That infuriated some Republicans, who said their party might have kept more seats in Congress and perhaps kept control of the Senate if Rumsfeld had left before the election.

Rumsfeld did not mention the Iraq war in his four-paragraph resignation letter.

Instead, the man who had become the focal point for critics of the Bush administration's management of the war, praised the president for his leadership.

"I leave with great respect for you and for the leadership you have provided during a most challenging time for our country. The focus, determination and perseverance you have so consistently provided have been needed and are impressive," Rumsfeld told Bush.

"It is time to conclude my service. As I do, I want you to know that you have my continuing and heartfelt support as you enter the final two years of your presidency," Rumsfeld wrote.

Rumsfeld also praised U.S. troops for their dedication, professionalism, courage and sacrifice.

Just days before the election, Bush told reporters he would like Rumsfeld to stay on for the rest of his presidency but later admitted he intentionally misled them.

"I know that one of the things that the president wanted to avoid was the appearance of trying to make this a political decision," White House spokeswoman Dana Perino told reporters in Crawford, Texas.

"And that was very important to him. And I think that the American people can appreciate not playing politics with such an important decision," she said.

MISSING LETTER?

Reuters obtained the letter from a U.S. official on Wednesday after the Pentagon in April said it did not have a copy.

Defense Department spokesmen repeatedly refused to release the resignation letter in November 2006.

Reuters then sought the letter twice under the Freedom of Information Act, a federal law that allows the public to seek release of government documents.

But in response to the request, the Defense Department said it did not have the letter. The White House office likely to hold the letter is not subject to FOIA, according to the White House's response in May to Reuters' FOIA request.

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