Sunday's demonstrations mark the 30th anniversary of a coup that brought Omar al-Bashir to power in 1989, toppling Sudan's last elected government. The military removed al-Bashir in April amid mass protests against his rule.
The military council has warned protest leaders that they will be held responsible for any destruction or damage by "vandals" and people "with an agenda" during the marches, AP reported.
The demonstrations come as the African Union and Ethiopia have accelerated their efforts to restart negotiations between the ruling generals and the protesters.
The talks collapsed when security forces violently broke up a protest camp in Khartoum earlier this month, killing over 100 people.