The opposition said dozens more have been injured during the demonstration – the latest in nearly four months of anti-government protests.
Around 20 people have been killed and dozens wounded in dawn attacks since Saturday on a sit-in outside Sudan's defence ministry by protesters calling for President Omar al Bashir to step down, the head of the main opposition party said on Tuesday.
Veteran leader Sadiq al Mahdi also called in a statement for "a select military command" to negotiate a transition towards democracy, following more than three months of protests that represent the most sustained challenge to Bashir's 30-year rule.
Some activists said in a statement posted on social media that army soldiers guarding the ministry were trying to protect the demonstrators and opened the gates of the compound to give sanctuary.
Sudanese intelligence and police forces attempted to break up the sit-in, setting off clashes with army troops in which a soldier was killed while trying to protect protesters, activists said.
TRT World's Philip Owira reports.
How did the latest protests start?
Thousands of protesters have massed at the army complex since Saturday, urging the military to back them in demanding the resignation of President Omar al Bashir and the formation of a transitional government.
It is the largest rally since protests erupted in the northeast African country in December over a hike in bread prices, before transforming into nationwide demonstrations against Bashir's iron-fisted 30-year rule.
"The security officers are firing heavy tear gas. I can see protesters coughing and covering their faces with hands and medical masks," a witness told AFP from near the site of the demonstration early Tuesday morning.
"I can also hear gunshots but it's unclear who is firing."
A protester at the complex also confirmed hearing gunshots but did not know who had fired.
An AFP correspondent, some five kilometres away from the protest site, heard shooting for about four minutes.
Protesters call for the army's help
Demonstrators have called on the army to protect them from the deadly crackdown, after days of camping outside the headquarters in Khartoum, which also houses Bashir's residence and the defence ministry.
"When the army is here, we have no fear," protesters chanted as military vehicles with soldiers fanned out around the complex, onlookers said.
Officials say 38 people have died in protest-related violence since December.
Defence Minister General Awad Ibnouf vowed to preserve the security and stability of Sudan.
"Sudan's armed forces understand the reasons for the demonstrations and is not against the demands and aspirations of the citizens, but it will not allow the country to fall into chaos," Ibnouf said, according to the official SUNA news agency.
"History will not forgive if the armed forces let the country lose its security."
In a separate statement, army chief of staff Kamal Abdelmarouf said the military was "discharging their responsibility in securing and protecting the citizens" together with other security forces.
The group spearheading the protests on Monday appealed to the army for talks on forming a transitional government.
"We call on the Sudanese armed forces to talk directly with the Alliance for Freedom and Change for facilitating the peaceful process of forming a transitional government," said Omar el Digeir, a senior member of the group.
Digeir said the protest organisers had also formed a council to initiate talks with security forces and the international community, aimed at agreeing to a "transitional government that represents the wish of the revolution".
"We reiterate our people's demand that the head of the regime and his government have to immediately step down," Digeir said.
Reading from a statement, he also called on the armed forces "to withdraw their support for a regime that has lost its legitimacy" and to support the "people's alternative for a transition to a civilian democratic government".
Since protests erupted across Sudan in December agents of the powerful National Intelligence and Security Service (NISS) and riot police have cracked down on demonstrators, but the army has not intervened.
Some activists on the ground accused the army of shooting in the air on Monday, but this could not be confirmed independently.
The rally outside the army headquarters has been the largest since protests began on December 19 in the central town of Atbara, quickly spreading to the capital and towns and cities across the east African country.
The European Union said an "unprecedented" number of people had come out calling for change since Saturday.
"The people of Sudan have shown remarkable resilience in the face of extraordinary obstacles over many years," the EU's External Action Service said.
"Their trust must be won through concrete action by the government."
The protesters accuse Bashir's administration of economic mismanagement that has led to soaring food prices and regular shortages of fuel and foreign currency.
Sudan's security council on Sunday said the demands of the protesters "have to be heard" after a meeting chaired by the veteran leader.
Bashir, wanted by the Hague-based International Criminal Court for alleged war crimes and genocide in the conflict-wracked region of Darfur, swept to power in a coup in 1989.
He has remained defiant, introducing tough measures that have seen protesters, opposition leaders, activists and journalists arrested.