The death toll from the worst earthquake to hit Myanmar in a century is expected to surpass 3,000 on Wednesday, as humanitarian agencies urged other countries to ramp up aid ahead of the monsoon rains.

Close to the epicentre, in the decimated cities of Mandalay and Sagaing, traumatised survivors slept in the street, with the stench of corpses trapped under the rubble permeating the disaster zone. Water, food and medicine are in short supply, and the monsoon could hit in May.

“The devastating impact of Friday’s earthquake is becoming clearer by the hour – this is a crisis on top of a crisis for Myanmar, where the humanitarian situation is already dire,” said Arif Noor, the Myanmar country director for the humanitarian agency Care.

“Rescue teams are still recovering those trapped under the rubble, and hospitals are overwhelmed. The physical and mental scars of this catastrophe will last for decades.”

Friday’s powerful quake is the latest in a succession of blows for the impoverished country of 53 million, which has been plagued by a civil war since the military seized power in a 2021 coup that has devastated the economy after a decade of development and tentative democracy.

The UN spokesperson Stephane Dujarric said: “We must act swiftly to provide relief before the upcoming monsoon season, which, of course, will even worsen this horrendous crisis.”

Myanmar’s military ruler, Min Aung Hlaing, said the death toll from the 7.7-magnitude quake had reached 2,719 as of Tuesday and was expected to pass 3,000. More than 4,500 people were injured and 441 remained missing. “Among the missing, most are assumed to be dead. There is a narrow chance for them to remain alive,” he said in a speech.

Some agencies say the unofficial toll could be as high as 10,000.

UN agencies said hospitals were overwhelmed and rescue efforts hindered by infrastructure damage and the civil war.

Julie Bishop, the UN special envoy for Myanmar, urged all sides to immediately cease fire, permit humanitarian access and ensure aid workers are safe. “Continuing military operations in disaster-affected areas risks further loss of life,” she said in a statement.

Residents and representatives of Myanmar’s exiled opposition National Unity Government (NUG) have accused the junta of continuing to drop bombs in the wake of the disaster, and of blocking emergency aid to areas that are beyond the military government’s control.

“[On Monday], five bombs were dropped around Nwe Khwe village. Although there were no casualties from that, the public is already traumatised by the earthquake,” said Ye Lay, 21, from Chaung-U, a town in the earthquake-affected region of Sagaing.

“Because of the earthquake damage people are staying outside their homes, and when bombs are dropped, they have to take shelter in trenches,” she said. “If an earthquake strikes, we can’t run away, so people are experiencing a profound sense of insecurity.”

Amnesty International said it had received testimony corroborating reports of airstrikes near areas where quake recovery efforts were focused. “You cannot ask for aid with one hand and bomb with the other,” said Amnesty’s Myanmar researcher Joe Freeman.

The Three Brotherhood Alliance of three major rebel groups at war with the junta on Tuesday declared a unilateral one-month ceasefire, to allow urgent humanitarian efforts to “be carried out as swiftly and effectively as possible”.

In its nightly news bulletin on Tuesday, the state-controlled MRTV quoted Min Aung Hlaing as saying the military had halted its offensives but that unspecified ethnic minority armies were planning to exploit the disaster.

“The military is aware they are gathering, training, and preparing to attack,” it said, quoting the general as saying at an event to raise funds for quake victims: “We consider it as attacking us and will respond accordingly.”

The junta has declared a week of national mourning, with flags to fly at half-mast on official buildings until 6 April “in sympathy for the loss of life and damages”.