"Jazz has always been a story of multi-culture," Atkinson said, before his band played for more than an hour in a set that featured Ellington's 'A' train, as well as a session with an Iraqi band that played traditional Arabic music.
Atkinson, whose tour has featured two other Iraq gigs, in Kurdish Arbil and in Ur, the renowned archaeological site and reputed birthplace of Abraham, flew into Baghdad in a Black Hawk helicopter at the invitation of the US embassy.
"When they offered me that trip, I thought twice, because I have a wife and a family," Atkinson said. "I thought I have to be cautious, but the (US) State Department is going to take care of me."
The musician, whose concert attracted a cosmopolitan crowd of about 400, featuring diplomats as well as Iraqi families gathered in the fortified Green Zone home of the Iraqi government, said he had seen "a little bit" of Baghdad.
"I had a ride on a Rhino (armoured bus) and a long Black Hawk tour. It was an enormous experience," he said.
The jazz musicians have already played in Yemen and Saudi Arabia and will continue their Middle East tour by visiting Lebanon.
"I love Middle Eastern music," Atkinson said, paying tribute to the late Iraqi oud maestro Munir Bachir.
"Take the 'A' train," written by Billy Strayhorn and named after a New York metro line, was a huge hit for Ellington, one of most influential figures in jazz who peformed in Baghdad in 1963.
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