The military "denies any sort of direct bombing inside the border of South Sudan," said an official from the foreign ministry.
Sudan's military has repeatedly rejected charges that its planes bombed across the border, and the latest incident came after the South ended a 10-day occupation of Sudan's main oilfield of Heglig.
Taban Deng, the governor of South Sudan's Unity State, said Sudanese bombs fell on a key bridge and a market, killing at least two children in the state capital Bentiu.
The bombs prompted heavy bursts of gunfire from Southern soldiers hoping to shoot down Khartoum's warplanes, said an AFP correspondent who was 50 metres from where the ordnance hit.
In the market, stalls were on fire and large plumes of grey smoke rose high into the air, as screaming civilians ran in panic.
The United States condemned the air raid and urged an "immediate" halt to hostilities and a return to talks, the State Department said.
France's foreign affairs spokesman Bernard Valero said the "aggression" was unacceptable and ran the risk of worsening the situation.
The latest raids dashed South Sudanese hopes for an end to weeks of fighting.
On Friday, Sudan's military declared it had forced Southern soldiers out of Heglig, after a 10-day occupation branded "illegal" by UN chief Ban Ki-moon.
South Sudanese President Salva Kiir had already announced that his forces would leave under "an orderly withdrawal." His army said the pullout was completed on Sunday.