South Sudan has accused Sudan of launching further bombing raids on its territory and against its forces.
The governor of Unity state says several people were killed in its capital Bentiu when a plane dropped bombs on a market. South Sudan also says its troops came under air attack in the oil-producing Heglig region which they have seized. Sudan's ambassador to the UK, Abdullahi Al Azreg, said Sudan did not target civilians.
He insisted Khartoum had bombed military camps used by northern rebels supported by South Sudan.
"These people are occupying our land. Everybody is witnessing what they are doing. They have killed the civilians, they are doing very bad things. We will target the rebels as long as they are occupying our land," he told the BBC. South Sudan said earlier on Saturday that it had repulsed an offensive on its positions near Heglig.
The events of the last week are a reversal of the expected order of things. Sudan has struggled militarily, despite its greater resources.
Its troops lost the Heglig oilfield – one of its biggest sources of revenue – and so far have not been able to take it back. The Sudanese forces' one great advantage – air power – has not tipped the balance in their favour. Sudanese political experts say the army's morale is low, and it is overstretched, as it has to fight South Sudan as well as several rebel movements who are co-ordinating together.
But – perhaps to its surprise – Sudan is winning the diplomatic war. The African Union said South Sudan's occupation of Heglig was "illegal and unacceptable".
Perhaps in reaction to these kind of statements, South Sudan then said it would withdraw its troops if UN peacekeepers were deployed to Heglig. This seems unlikely, and South Sudan simply hasn't been able to convince the world it's in the right.
So for the moment South Sudan is in the unusual position of winning the fighting – and losing the war of perceptions.
Vice-President Riek Machar said the ground fighting took place on Friday 30km (18 miles) north of Heglig. South Sudan seized the oil field on Tuesday, sparking international condemnation and fears of a wider war with its northern neighbour.
South Sudan entered the oil field in response to what it said were attacks from north of the border.
Sudan's leaders are furious after its southern neighbour took over the Heglig oilfield, which is internationally recognised as Sudanese territory. The African Union has demanded an unconditional withdrawal.
The South seceded nine months ago in a deal that ended decades of civil war, but there remain a number of major disputes, including oil.
'Good news soon'
Sudan's army confirmed on Friday it was launching attacks to retake Heglig after the Khartoum government vowed to react with "all means" against the offensive by South Sudanese forces.
And Sudanese army spokesman Col Sawarmi Khalid said on Saturday Heglig region was "100%" under their control.
"We are now inside Heglig and we can talk about a few kilometres separating us from the Heglig oilfield." But Mr Machar told the BBC his country's soldiers had now pushed Sudanese troops back to Karasana, north of Heglig. South Sudanese Information Minister Barnaba Marial Benjamin told Reuters on Saturday: "They tried to attack our positions north of Heglig last night but it was contained. Heglig is [still] under our control."
South Sudan's military spokesman, Col Philip Aguer, told Agence France-Presse two Sudanese tanks had been destroyed.
There is no independent confirmation of the South's claims.
South Sudan took most of the oil fields when it seceded from Sudan last July
But it has to export its oil using pipelines through ports in Sudan's territory
South Sudan depends on oil sales for 98% of its revenue; transit fees account for 36% of Sudan's budget
South Sudan stopped pumping oil in January in a row over transit fees, accusing Sudan of stealing oil worth $815m (£518m)
Heglig, Sudan's biggest oil field, was awarded to Khartoum by the Permanent Court of Arbitration in 2009
South Sudan accuses Sudan of using Heglig to launch attacks on its oil installations
'Deep alarm'
The BBC's James Copnall, in Khartoum, says it seems likely there will be further battles and what started out as a border skirmish now seems perilously close to becoming an all-out war.
Heglig is vital because it accounts for about half of Sudan's 115,000 barrel-a-day oil output and the fighting has stopped production there.
The African Union's Peace and Security Council has called the occupation of Heglig "illegal and unacceptable", but also condemned Sudan for carrying out aerial bombardments of South Sudan.
On Thursday, the UN Security Council called for an "immediate" ceasefire and expressed "deep and growing alarm at the escalating conflict".
Via BBC