The demonstrations are the biggest in several years against Bashir's 29-year rule, with protesters enraged over inflation, shortages of basic goods and a cash crisis.
Amnesty International says it has "credible reports" that Sudanese police have killed 37 protesters in clashes during anti-government demonstrations that erupted last week across much of the country.
In a statement late Monday, the London-based rights group said the use of lethal force by security forces against unarmed protesters was "extremely troubling" given that more protests were planned Tuesday.
A coalition of independent professional unions has called for a march on the presidential palace in Khartoum later Tuesday to submit a petition demanding that longtime autocrat Omar Bashir step down.
Two of Sudan's largest political parties called on their supporters to take part.
The protests began last Wednesday, initially over rising prices and shortages of food and fuel, but later escalated into calls for Bashir to go.