Khartoum dismissed the allegations as “incorrect.”
“Those who are killed are innocent civilians who are looking after their cattle,” South Sudan’s military spokesman Philip Aguer told AFP, adding that the casualties came on the second day of bombing in the Boro El Madina area.
“This information is completely incorrect,” the Sudanese military spokesman Sawarmi Khaled Saad said in Khartoum.
In a separate statement, Sudan’s foreign ministry alleged that 350 members of Darfur-based rebel group the Justice and Equality Movement (JEM) had crossed into South Sudan on Wednesday.
The ministry’s spokesman, Al-Obeid Meruh, called on the international community to pressure “the government of South Sudan to stop supporting these troops and disarm them.”
South Sudan separated from Sudan in July after an overwhelming vote for independence that followed more than two decades of civil war.
Each side has accused the other of supporting rebels inside its borders.
Aguer said bombing had resumed over the past two days around Jau, a disputed area along the South Kordofan-Unity state border.
There were no casualty reports from that area “because the bombing was intensive,” he said.
“SPLA has placed its forces on maximum alert” since Christmas, he said, referring to the Sudan People’s Liberation Army.
“The intention of Khartoum is to annex some of these areas.”
Sudan’s military spokesman, Saad, in turn accused South Sudan of building up its own troops in the Jau area to attack inside Sudan.
Access to the areas is restricted, making independent confirmation of the claims difficult.
United Nations peacekeepers are based in South Sudan, but AFP was unable to reach any officials from the mission.
Oil-producing South Kordofan remained under Khartoum’s administration when South Sudan became independent, but fighting since June has pitted Nuba rebels, once allied to rebels in the south, against the Sudanese army.
A conflict also broke out three months later in nearby Blue Nile state.
The UN says 300,000 people have been internally displaced or otherwise severely affected by the fighting in South Kordofan, with 20,000 having fled to South Sudan.
Khartoum’s allegation that JEM rebels had entered South Sudan came days after the killing by government forces of the group’s leader Khalil Ibrahim, creating uncertainty as to the future of what was Darfur’s most heavily armed group.