Witnesses told the news agency that security forces used tear gas against dozens of demonstrators in al-Halfaya Bahri, an area in the south of Khartoum, and against a demonstration by dozens of people emerging from Sayed Abdel Rahman Mosque in Omdurman, which sits on the other side of the River Nile from the capital.
Human Rights Watch also said that at least 40 people, including children, have been killed in the protests, citing Sudanese activists and medical workers.
Women protesters, many wearing masks to protect themselves from tear gas, whistled and clapped as they marched in the streets of Bahari, the hub of Sunday's demonstration. The footage could not be independently verified.
In response to the demonstrations, riot police and security agents have broken up the rallies by firing live ammunition and volleys of tear gas, rights groups reported.
Later, loud bangs, said to be gunfire, are heard as the camera holder and others flee.Protests were also held in other areas of the country including, for the first time, Nyala, the main city in Darfur, according to Reuters.Hundreds have participated in Sudan's ongoing protests, according to Reuters.
Protesters there took to the streets of El-Fasher, the capital of North Darfur state.
A demonstrator wearing a shirt that in Arabic reads "I am a peaceful protester" takes part in an anti-government rally in the capital Khartoum on January 13, 2019.
Darfur, a region the size of France, has been torn by violence since 2003 when ethnic minority rebels took up arms against Khartoum, accusing it of economic and political marginalisation.
Al-Bashir, who has been ruling the country since a military coup in 1989 and remains wanted by the International Court of Justice for war crimes, has blamed the protests against his government on "conspirators".
Sudan has been rocked by protests since mid-December, with demonstrators decrying the government's seeming inability to rein in rampant inflation and acute commodity shortages.
The demonstration was the first of its kind in Darfur since the unrest began.
Last month, the United States, Britain, Norway and Canada said in a joint statement that they have "reliable reports" that Sudan's security forces were using live fire.
The crisis has deepened since a year ago, when the country saw some brief protests over bread shortages.
Repeated shortages of food and fuel have been reported in several cities, including Khartoum, while the costs of foods and medicines have more than doubled.
The US imposed a trade embargo on Khartoum in 1997 that was lifted only in October 2017. It restricted Sudan from conducting worldwide business and financial transactions.
"We condemn using bullets against citizens", said the commission, whose members are appointed by President Omar al-Bashir.