WASHINGTON, June 30 (Reuters) - Tuesday was a day of celebration in Iraq as U.S. forces handed control of the cities to Iraqi authorities, but the top U.S. commander was less than joyous when pressed on how many of his troops would remain.

Speaking via satellite from Baghdad, U.S. Army General Ray Odierno lost his cool at a briefing for Pentagon reporters when he was repeatedly questioned about the number of U.S. troops that would remain in the cities as advisers to Iraqi forces.

Asked why he could not give a figure, he became visibly irritated, raised his voice and replied: "Because it would be inaccurate! Because I don't know exactly how many are in the cities. It varies day-to-day based on the mission."

Pressed to give a rough figure, he snapped: "How many times you want me to say that? I don't know."

Odierno, one of the most formidable figures in the U.S. military, apologized for his outburst at the end of the briefing.

"Sorry I lost my temper a little bit on the number," he said, to some laughter from reporters. (Reporting by Andrew Gray)

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