Protests that first erupted across Sudan on December 19 over a government decision to triple the price of bread have swiftly escalated into broader demonstrations against al-Bashir's three-decade rule.
Protest organizers have called for near daily demonstrations across the country against Bashir this week, calling it a "Week of Uprising".
The group called for a major rally in Khartoum North on Sunday, to be followed by further demonstrations in the capital during the week.
Anti-government protests first flared last month and have posed the most serious challenge yet to Bashir, a former army general who is wanted by the International Criminal Court for alleged war crimes in the Darfur region.
"The Government of Sudan must also take immediate action to stop the practice of shooting protesters and respect the Sudanese people's right to freedom of expression", said Sarah Jackson, the human rights group's Deputy Director for East Africa.
"But so far there hasn't been an escalation, they are persistent but they haven't risen in intensity in a significant way".
The crisis has deepened since a year ago, when the country saw some brief protests over bread shortages.More news: Authorities Identify Deceased Suspect in Davis Officer Natalie Corona's Murder
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Repeated shortages of food and fuel have been reported in several cities, including the capital, Khartoum, while the cost of food and medicine has more than doubled.
The United States lifted 20-year-old trade sanctions on Sudan in October 2017, but many investors continue to shun a country still listed by Washington as a state sponsor of terrorism.
In a strongly-worded statement, Sudan's National Commission for Human Rights slammed the attack on the Omdurman hospital and called for a swift investigation into the deaths of citizens.
Sudan's economy was crippled when the south seceded in 2011, taking away much of its oil resources.
The president has remained defiant telling thousands of loyalists at a Khartoum rally on Wednesday that his government would not give in to economic pressure.
In a joint statement on Tuesday last week, the United States, United Kingdom, Norway and Canada condemned the violence and said Sudan's "actions and decisions over the coming weeks will have an impact on the engagement of our governments and others in the coming months and years", referring to ongoing efforts by the USA and UK to normalise relations with Sudan.
In previous weeks, demonstrations have begun only after sundown and the number of people at this Friday's protests appeared smaller than in the past.