Angry crowds have taken to the streets in a dozen cities across the economically troubled country since Wednesday after the government tripled the price of bread.
The authorities say that eight protesters have been killed in clashes, but Amnesty International has put the death toll at 37.
Police vehicles and officers with batons could be seen around the capital Khartoum as authorities braced for a further challenge to Bashir's decades-long rule.
An AFP journalist saw security officers stationed on the roofs of building along the expected route of Tuesday's march, which was called by an umbrella labour group.
Doctors went on strike Monday and the group bringing together professionals from different sectors pledged to submit an official demand for Bashir's resignation at Tuesday's demonstration.
Bashir, who has been in power since a 1989 coup, sought to tamp down the discontent by pledging Monday to "take real reforms" to solve Sudan's economic woes.
The veteran leader on Tuesday headed south of Khartoum to Gezira state, where dozens of protesters have called for him to go.
Sudan is mired in economic difficulties including an acute foreign currency shortage and soaring inflation.
The crisis has worsened despite the lifting of an economic embargo by the United States last October.
Inflation is running at close to 70 percent and the Sudanese pound has plunged in value, while shortages have been reported across several cities including Khartoum.
Bashir's party is pushing for him to stand again in 2020 elections, a move that would violate constitutional term limits.
Agencies contributed to this report.
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