Bashir's remarks come amid an ongoing dispute between the Sudanese government and Unamid over six people wanted by Khartoum.
The Sudanese government accuses the six members of the Sudan Liberation Army (SLA), one of the rebel groups most hostile to the Sudanese government, of starting a clash last month in the Kalma camp.
Kalma houses more than 100,000 people who fled their homes during years of bloody rampages carried out by militias in western Sudan.
"The camps are Sudanese territory under Sudanese authority and there is no authority in this world which can stop the government from ... prosecuting criminals who break the law," Bashir said.
Eleven people were killed in last month's fighting in Kalma, which involved the SLA and the Liberation and Justice Movement (LJM). The LJM is currently talking with the government in Khartoum.
Unamid earlier this month refused to hand over the SLA suspects, and accused the government of blocking shipments of humanitarian aid to Kalma.
Ibrahim Gambari, the head of Unamid, met with Sudanese officials last week and said he would not turn over the suspects without proof of their crimes or guarantees of a fair trial.