The move comes a day after a pro-democracy sit-in was violently overrun by the military, leaving at least 35 people dead, according to protest organisers.
The leaders of the pro-democracy movement, who demand that a civilian government take over the running of the country, said they were stopping all contact with the Transitional Military Council (TMC) and called a general strike.
Shams al-Deen al-Kabashi, spokesman for the council, acknowledged the operation in televised remarks but said the military was targeting just one area of the protests, nicknamed "Colombia" by protesters because of prolific drug use that happens there.
The SPA said Monday's action against the sit-in amounted to a "bloody massacre".
"What is clear to us is that there was use of excessive force by the security forces on civilians".
The US said it was a "brutal attack" while the United Kingdom called it "outrageous".
For the masses of Sudanese workers and poor, the way forward lies not through the calls by the bourgeois- and petty-bourgeois-led opposition for a civilian-led transitional government, which would also serve as a façade for the continued rule of Sudan's small, wealthy elite and its military henchmen.
On Saturday, the ruling TMC issued a statement declaring that the "sit-in has become a threat to the country".
Sudan's public prosecutor on Monday ordered an investigation into the violence, state news agency SUNA said.
"We gathered in our square as we usually do every year but the Rapid Support Forces and the police fired teargas and sound bombs at us and after the prayers the youth closed the main street by putting up barricades", a resident of the Bahri area told AFP. The RSF is led by Lt. Gen. Hamdan Dagalo (popularly known as "Hemeti"), the deputy chair of the country's now ruling junta, the Transitional Military Council (TMC), and widely viewed as an aspiring dictator.
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The protest-linked doctors group said security forces had surrounded one Khartoum hospital and had opened fire at another where they were pursuing protesters.
A broad swath of Sudanese society has staged a sit-in in Khartoum since April 6, just days before the military toppled President Omar Hassan al-Bashir, who had led the country for 30 years.
Protesters have remained camped out in front of Khartoum's army headquarters to pressure the generals to yield power. Protestors said they themselves were peaceful and unarmed.
Burhan said elections would be held within nine months.
He asked the Sudanese authorities to facilitate an independent investigation and ensure that those responsible are held accountable.
"The TMC can not responsibly lead the people of Sudan", the Embassy said on Twitter.
The sit-in near the army headquarters has been the epicenter of protests demanding the TMC hand over power to a civilian government.
In a speech made in the first hours of Tuesday morning, al-Burhan accused the opposition Forces for Freedom and Change (FFC) of bearing the responsibility for prolonging the negotiations on power handover and trying to exclude the other political and military forces before to "clone another totalitarian regime", as he said.
Streets around the city centre were nearly deserted Tuesday, with many markets and shops closed and nearly no cars on the roads on an overcast morning. Neighboring Egypt called for "calm and restraint", while the United Arab Emirates (UAE) said it hoped that dialogue would prevail in Sudan.
An worldwide rights group is calling for the United Nations to launch an "impartial, independent" investigation into the Sudanese military's recent crackdown on pro-democracy protesters that killed at least 35 people.