Mediators admitted the truce had been "imperfectly observed".
UN Secretary-General Antonio Guterres reiterated his support for the body's envoy to Sudan after Burhan called for his dismissal.
Darfur has never recovered from the years-long war that began in 2003.
The United States on Thursday said it will only be ready to mediate a truce between Sudan's warring parties when they get "serious", after the army left negotiations and the latest ceasefire unravelled.
The army on Wednesday blasted bases of the paramilitary Rapid Support Forces (RSF) after pulling out of the truce talks in the Saudi city of Jeddah, accusing its rival of breaching the ceasefire meant to bring in aid.
The United States said there had been "serious violations of the ceasefire by both sides".
"Once the forces make clear by their actions that they are serious about complying with the ceasefire, the United States and the Kingdom of Saudi Arabia are prepared to resume facilitation of the suspended discussions to find a negotiated solution to this conflict," a US State Department spokesperson said.
"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," he said.
In both north and south Khartoum on Wednesday, troops loyal to army chief Abdel Fattah al-Burhan attacked key bases of the RSF led by commander Mohamed Hamdan Daglo, residents told AFP.
One witness said there was "heavy artillery fire from army camps" in the capital's north, on the 47th day of a war that researchers said has claimed 1,800 lives.
Another reported "artillery blasts on the RSF camp in Al-Salha" in southern Khartoum -- the largest paramilitary base and arsenal in the city.
The attacks came two days after United States and Saudi mediators said the warring parties had agreed to extend by five days the initial week-long humanitarian truce.
The mediators of the talks in Jeddah acknowledged repeated breaches but have held off imposing any sanctions.
Army walks out
“The army walked out because the rebels have never implemented a single one of the provisions of a short-term ceasefire which required their withdrawal from hospitals and residential buildings,” a Sudanese government official said on condition of anonymity.
Mediators admitted the truce had been "imperfectly observed", but said the extension would "permit further humanitarian efforts". Despite repeated pledges from both sides, fighting has flared this week both in greater Khartoum and in the western region of Darfur.
"The army is ready to fight until victory," Burhan declared during a visit to troops in the capital.
The RSF said they would "exercise their right to defend themselves" and accused the army of violating the truce. African Union spokesman Mohamed El Hacen Lebatt told AFP that suspension of the talks should "not discourage" mediation efforts.
Guterres reiterates support
UN Secretary-General Antonio Guterres on Wednesday reiterated his support for the body's envoy to Sudan, Volker Perthes, after Burhan called for his dismissal.
"It is up to the Security Council to decide whether the Security Council supports the continuation of the mission for another period or whether the Security Council decides that it is time to end it," he said.
After a meeting with East African bloc IGAD, and other officials, he said a plan for broad talks among all Sudanese would be proposed as soon as possible.
Since fighting erupted on April 15, more than 1,800 people have been killed, according to the Armed Conflict Location and Event Data Project.
The UN says 1.2 million people have been internally displaced and more than 425,000 have fled to neighbouring countries.
Yaqout Abderrahim escaped Khartoum for Port Sudan, where she has been waiting 15 days for a rare seat on a flight out. "We want to leave at any price because our houses are destroyed and we no longer have any means to raise our children," she told AFP among families camped out on the ground.
More than half the population -- 25 million people -- are now in need of aid and protection, the UN says.
Entire districts of Khartoum no longer have running water, electricity is only available for a few hours a week, and three quarters of hospitals in combat zones are not functioning.
The health ministry said Wednesday that "nine health facilities" had gone out of service in Jazira state, just south of Khartoum, "despite the declared truce".
It blamed "the presence of RSF militias threatening the movement of medical personnel and supplies".
"Hundreds have been killed in Darfur, on Sudan's western border with Chad, where continued fighting blatantly disregards ceasefire commitments," Toby Harward, of the UN refugee agency, said earlier.
Darfur has never recovered from the years-long war that began in 2003 when a rebel uprising led strongman Omar al-Bashir to unleash the Janjaweed militia, from which the RSF are descended.
Experts say Burhan is facing increasing pressure from his own Islamist supporters and remnants of the Bashir regime, with whom he had built a symbiotic relationship in order to gain power.
