By Dean Yates

EAST OF BAQUBA, Iraq, Oct 7 (Reuters) - The U.S. military commander in Iraq, General David Petraeus, suggested over the weekend that security had improved enough in Baghdad for him to walk parts of the capital's streets without protection.

"Arguably you could do that now," Petraeus told a small group of reporters at a U.S. military base in Diyala province on Saturday when asked if there would come a day when he could walk the capital's streets without plenty of armed guards.

"Nobody will let me do it," he said, smiling.

Asked if he was serious, Petraeus said: "Certainly in places you could do that. You could walk right down Haifa street right now."

Haifa street is in central Baghdad and was a hotbed of insurgent activity where clashes often broke out.

A U.S.-backed security crackdown, launched in February with the aid of 30,000 additional American troops, has helped bring down levels of violence in Baghdad.

But bombings and sectarian death squad killings still occur and Iraqis say they are constantly fearful. Three bombings killed eight people in Baghdad on Sunday.

Petraeus, an easygoing four-star general, likes to get out among Iraqis and see the situation on the ground for himself. He is heavily protected on such outings.

Petraeus said he did not want to sound naive. He referred to a roadside bomb attack on the convoy of the Polish ambassador in Baghdad last week that wounded the envoy.

"The problem of course is that there is the ever present, there is the always lurking (threat) as happened tragically to the Polish ambassador," said Petraeus.

Asked if he thought it was safe for Westerners to walk along Baghdad's streets without armed guards, Petraeus was cautious:

"No I don't ... I don't know how many times out of a 100 you could do it before there (would be) problems," he said.

"I don't want to appear to be naive. If you say will there be a time when you can walk around Baghdad? Obviously I hope that will be realised in the future."

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