Three protesters have been killed during an anti-government demonstration in Sudan even as thousands chanted support for President Omar al-Bashir at a rival rally in the capital, Khartoum.

Sudan's official SUNA news agency on Wednesday said Khartoum's twin city, Omdurman, "witnessed riots and illegal gatherings" that were dispersed by tear gas.

Police spokesman Hashim Abdelrahim confirmed that three protesters had died and several injured during the anti-government demonstrations.

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"We are investigating," he said, without specifying how the protesters died.

Wednesday's competing rallies in Sudan followed a month of angry street protests over a government decision to triple the price of bread at a time when the country faces an acute shortage of foreign currency and a high inflation rate of 70 percent.

Authorities say at least 22 people, including two security personnel, have been killed since December 19 during the demonstrations. Human Rights Watch has put the death toll at 40.

On Wednesday, about 300 protesters, chanting "freedom, peace and justice", blocked a key road in Omdurman, but were quickly confronted with tear gas as riot police moved in to disperse them.

Protesters are demanding the removal of President Bashir, the 74-year-old general-turned-politician, who has ruled the North African state since 1989.

More than 800 people have been arrested since the unrest began, said officials, insisting that the situation has now stabilised even as protests rumbled on.

Separately, supporters of Bashir staged a rally in Khartoum on Wednesday.

Dressed in a khaki shirt and trousers and waving a stick, a smiling Bashir greeted the cheering crowd as men and women, who arrived in buses from early in the morning, whistled and waved flags.

Sudan's ruling party has pressed ahead with plans to change the constitution, so Bashir can stay in office beyond his present term, which ends in 2020.