Sudanese opposition groups on Wednesday rejected the army’s offer of talks as Saudi Arabia urged the sides to return to the table.
The death toll from the clearing of a protest camp outside the Defence Ministry in Khartoum has reached 108.
The Transitional Military Council said it was conducting an investigation into the deaths and those who had crossed the line would be held accountable.
The military on Wednesday said it was willing to restart talks without conditions but Madani Madani, who leads the Declaration of Freedom and Change Forces, said protesters were not prepared to hold discussions while there was violence in the streets.
"We do not accept the Transitional Military Council's invitation because it is not a source of trust," Mr Madani said. "It is imposing fear on citizens in the streets."
The UN announced it was moving some of its staff from the country, a spokeswoman said.
"We are temporarily relocating non-programme-critical UN staff, while all UN operations continue in Sudan," Eri Kaneko said.
No details were provided on the number of staffers leaving Khartoum, where there is a large UN presence of 27 bodies, mostly aid agencies.
The UN also runs a peacekeeping mission in Darfur with the African Union, where about 7,200 troops and police are posted.
On Wednesday, Britain also warned its citizens against all but essential travel to Khartoum as it pulled non-essential staff and their dependants from its embassy.
Saudi Arabia said it was watching the unfolding situation with concern and that talks were the only way to ensure stability and security for the Sudanese people.
"The kingdom hopes that all parties in Sudan will choose wisdom and constructive dialogue to preserve security and stability in Sudan, protect the people of Sudan from all harm, while maintaining Sudan's interests and unity," the official Saudi Press Agency said on Wednesday.
"The kingdom affirms the importance of resuming the dialogue between the various parties in Sudan to fulfil the aspirations of the brotherly Sudanese people."
Riyadh has close links to the Sudanese military, which has sent troops to fight in Yemen as part of the coalition to restore the rule of the internationally recognised government of President Abdrabu Mansur Hadi.
Saudi and the UAE also announced a major aid package of $3bn to help stabilise the economy after longtime leader Omar Al Bashir was removed from office in April.
Amid growing international concern, US undersecretary of state David Hale called Saudi deputy defence minister Khalid bin Salman about the June 3 break-up of the protesters' camp.
US National Security Adviser John Bolton also criticised the military response.
But after years of US sanctions on Khartoum, Washington has little influence in Sudan.
Talks between the Transitional Military Council, which has ruled since president Mr Al Bashir was removed, and the opposition ground to a halt amid deep differences over who would lead a three-year transition to democracy.
Then this week, the council said it had intervened at the sit-in protest outside Sudan's Defence Ministry against "criminal elements".
The camp formed in the final weeks of Mr Al Bashir’s rule and has been the focal point for demonstrations.
At least 40 civilian bodies have been recovered from the Nile River, which separates the capital Khartoum from sister city Omdurman, the Sudan Doctors Committee said on Wednesday.
The group called for all doctors to race to local hospitals in Khartoum and Omdurman, saying violence was continuing.
A prominent anti-government politician, Yasir Arman, was beaten and arrested by Sudanese security forces during the violence, the British ambassador to Sudan, Irfan Siddiq, tweeted on Wednesday.
The deputy head of the Transitional Military Council said it had launched an investigation into the violence.
"The council has initiated an independent investigation, an urgent and transparent investigation with fast results," said the council's deputy chairman, Gen Mohamed Dagalo.
"Any person who crossed boundaries has to be punished."
Gen Dagalo met Saudi Crown Prince Mohammed bin Salman in Jeddah in May during a regional tour.
Mr Arman is the deputy chairman of the Sudan People's Liberation Movement-North, which has been fighting government forces since 2011
He had been sentenced to death in his absence and was living in exile. But shortly after Mr Al Bashir was removed from power, he returned to Sudan to attend talks with the military council.
Mr Siddiq called the arrest outrageous and asked for his immediate release, saying the military would not be able to rebuild trust if it continued to hold him in detention.
Mr Siddiq said the internet had been out in Sudan since June 3.
"The authorities must turn the internet back on and keep phone lines open," he said.
On Tuesday, the military council said it would hold elections within nine months under international observation, but protest groups rejected this plan, saying they wanted more time and a civilian-led interim government.
"It's not the putschist council, nor its militias, nor its leaders who decide the fate of the people, nor how it will transition to a civilian government," said the Sudanese Professionals Association, a leading group in the protest.
China and Russia blocked a bid at the UN Security Council on Tuesday to condemn the killing of civilians in Sudan and issue a pressing call from world powers for an immediate halt to the violence, diplomats said.
During a closed-door council meeting, Britain and Germany circulated a statement that would have called on Sudan's military rulers and protesters to find a solution to the crisis.
But China objected to the proposed text while Russia insisted that the council should await a response from the African Union.
After the statement was blocked, eight European countries –Belgium, Britain, France, Germany, Italy, Poland, The Netherlands and Sweden – issued their own statement criticising the attacks on the protesters.
On Monday, paramilitary forces connected to the military council stormed the main protest site outside the country's defence ministry, opening fire and beating people with large sticks.
Meanwhile, the military council denied they had blocked ambulances from reaching wounded civilians, and expressed regret over the turn of events.