The note was written with a pen on the inside of the boat as he lay bleeding from an earlier shootout with police in which his brother Tamerlan Tsarnaev was killed, sources told CBS.
"When you attack one Muslim, you attack all Muslims," he allegedly wrote, saying the bombings were revenge for Iraqis and Afghans killed during U.S. military conflicts in those countries.
Dzhokhar Tsarnaev said he didn't mourn his brother because Tamerlan was a martyr in paradise and he expected to join him soon.
The interior of the boat hull on which the note was written was riddled with holes from bullets fired by police who thought Dzhokhar Tsarnaev had another bomb, CBS said.
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