Saudi Arabia and the U.S. have listed serious violations of the cease-fire by both sides.
"These violations have led us as a facilitator of these talks to seriously question whether the parties are ready to take the actions needed to meet the obligations they have undertaken on behalf of the Sudanese people," a U.S. State Department official said.
Witnesses reported an increase in fighting early on Thursday in various parts of the capital, which is composed of Khartoum and its twin cities of Bahri and Omdurman around the confluence of the River Nile and is one of Africa's largest urban areas.
Residents said heavy artillery fire could be heard in northern Omdurman and intermittent firing in southern Bahri.
Clashes also continued near a market in southern Khartoum, where at least 19 people were killed and 106 injured on Wednesday, according to a member of a local neighborhood committee.
He said that the number of dead and injured was higher than tallied since several people had been treated or buried at home by relatives wary of venturing to hospital.
Outside Khartoum, clashes have flared in major cities in the western region of Darfur. A regional rights group said at least 50 people have been killed in the last week in the westernmost city of El Geneina which has already seen hundreds killed in militia attacks.
In the city of Zalingei, it said that city's hospital and university were looted and people were being killed "randomly."
Residents said heavy artillery fire could be heard in northern Omdurman and intermittent firing in southern Bahri.
"We are being terrorized by the sounds of heavy artillery around us. The house has been shaking," said 49-year-old Nadir Ahmed in the Thawra neighborhood of Omdurman. "Where is this cease-fire we hear about?"
On Wednesday, the army announced it was pulling out of talks in the Saudi city of Jeddah where the cease-fire deal was struck and where mediators had been trying to bolster and prolong the truce.
Meanwhile, the calm Red Sea coast city Port Sudan has served as a base for the United Nations, aid groups, and diplomats as well as some government officials.
However, a curfew was declared in the city earlier this week as the army warned of "sleeper cells" sneaking into the city. Residents say that buses into the city, which is a key evacuation point, have been blocked.
"The army is carrying out strict security procedures in the city, in particular at night," said resident Salah Mohamed.