The latter was the most popular slogan of the 2010 and 2011 Arab Spring revolts.
Medical sources speaking to Sudan Tribune in Khartoum said 8 protesters were injured by fire bullets, pointing out that 4 of them are in critical condition.
Amnesty International said it had "credible reports" that security forces had used live ammunition on demonstrators, killing a total of 37 over the last week.
Sudanese authorities have announced a state of emergency and curfew in a number of provinces over the protests, with government officials accusing Israel of plotting with rebel groups to cause violence in the country.
The protests began last Wednesday, initially over rising prices and shortages of food and fuel, but later escalated into calls for Mr Al Bashir to go.
He will travel to the state's north to open a hospital, avoiding a visit to its capital Madani which was one of the central locations of unrest during a wave of similar protests in September 2013, when scores of people were killed in the city.
Video footage showed protesters with gunshot wounds, including one who had been hit in the head, and police snipers on rooftops near the palace that was built on the bank of the Blue Nile using funds from China. Besides, they also attempted to attack a government building, but were turned back by security officials.
Oil prices surge as United States equities soar
The contract settled 5.3% lower to end at $1.2488 a gallon on Monday, booking its lowest settlement since February 29, 2016. They slumped 6.7% in the previous session to US$42.53 a barrel, the lowest since June 2017.
The situation in Sudan is taking a turn for worse, as the protests by a coalition of unions continue.
The military vowed on Sunday to rally behind Bashir and emphasized in a statement that it was operating in harmony with the police and Sudan's feared security agencies.
On Monday, Bashir said his government is working on to introduce measures to stabilize the economy and "provide citizens with a dignified life".
Sudan government has also shut down the internet since December 20, in an attempt to stop the protests from reaching global audience.
Indicted by the International Criminal Court for crimes against humanity, war crimes and genocide in Sudan's western Darfur provinces, Bashir is seen by experts as an authoritarian and volatile leader.
Bashir's party is pushing for him to stand again in 2020 elections, a move that would violate constitutional term limits.