Bloodied people screaming for help were running out of buildings billowing with smoke, they said. Trader Mallam Samalia said some people were blown apart.
The second blast caught people trying to help those injured in the first explosion in the Bintu-Suga neighborhood of the Ngomari suburb, he said.
It appeared to be a car bomb, from a pickup truck loaded with wood, Samalia told The Associated Press by telephone. "I'm seeing people carrying bloody bodies," he said. "There are parts of bodies littering the street."
The police commissioner did not immediately answer his phone to confirm the reports.
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It was the first attack in months in Maiduguri, capital of Borno state and the headquarters of a military force tasked with suppressing the 4-year-old Islamic uprising that has killed thousands.
More than 300 people were killed in February alone in attacks increasing in frequency and deadliness, all in the neighboring states of Yobe and Adamawa.
That anger will be fueled by reports that a military fighter jet targeting extremist hideouts bombed a village in Yobe state and killed at least 20 civilians on Friday, according to survivors.
Borno, Yobe and Adamawa state cover one-sixth of Nigeria and have been under a state of emergency since May.