Two protesters were shot dead by the security forces in Omdurman while thousands of people marched towards the presidential palace in the Sudanese capital Khartoum.
Sudanese security forces have killed two protesters in Omdurman, twin city of the capital Khartoum, medics said, as thousands rallied against the military.
The pro-democracy Doctors' Committee said on Sunday that one of the protesters was shot in the chest while the second suffered a "severe head wound".
Earlier on Sunday, Sudanese security forces fired tear gas canisters at a thousands-strong rally outside the presidential palace in Khartoum demanding civilian rule.
The demonstrators marched in the 12th round of major protests since the October 25 coup launched by military leader General Abdel Fattah al Burhan
Demonstrators were shouting "power to the people" and demanding a return of the "military to the barracks".
Sunday's deaths bring the total number of protesters killed in a violent crackdown since a military takeover in October to 56, while hundreds have been wounded.
Gripped by turmoil
Sudanese authorities had also cut mobile internet services earlier on Sunday amid calls for pro-democracy rallies in "memory of the martyrs" killed in recent protests.
Web monitoring group NetBlocks said the mobile internet was cut from mid-morning ahead of the planned protests, the first of the year.
Activists use the internet for organising demonstrations and broadcasting live footage of the rallies.
Sudan has been gripped by turmoil since military leader General Burhan launched a coup and detained Prime Minister Abdalla Hamdok.
Hamdok was reinstated on November 21, but mass protests have continued as demonstrators distrust veteran general Burhan and his promises of seeking to guide the country toward full democracy.
Activists have kept up a more than two-month-long campaign of street demonstrations against the army's takeover.
Burhan denies the takeover was a coup, and on Friday, a close advisor warned that "the demonstrations are only a waste of energy and time" which will not produce "any political solution".