Salva Kiir, South Sudan's president, has denied that his armed forces damaged the contested Heglig oilfield they seized for 10 days earlier this month because it belongs to South Sudan.
"Panthou and the oil on top of it is ours ... it is impossible that we would damage or destroy [the facilities]," Kiir, using South Sudan's name for the Heglig oilfield, told tens of thousands of supporters on Friday after his return from China.
Both South Sudan, which seceded from Sudan and became independent last July, and Sudan claim the Heglig oilfield. South Sudan said its forces withdrew from the area last Friday after coming under intense diplomatic pressure to pull back.
"One day, if there is law in this world, Panthou will come back to us by law ... That's why this talk about us damaging [the oilfield] is a lie," he said.
"We have no reason to damage the oil refineries in Panthou or any other contested areas because these areas are ours."
Satellite images have shown serious damage to some of the infrastructure. Each side has accused the other of damaging the facilities, part of a war of words that has accompanied local fighting along the 1,800 km (1,100 mile) contested border in what was once Africa's largest country.
Fighting across the disputed border erupted in late March after Sudan and South Sudan failed to resolve a number of contentious issues including oil export fees and citizenship.
Since pulling out from Heglig, South Sudan has accused Khartoum of cross-border air raids, which Sudan denies.
Earlier on Friday South Sudan said a Sudanese-backed rebel militia had attacked a town in the South's oil-producing Upper Nile state, potentially broadening the conflict.
"A militia that is supported by the Sudanese Armed Forces attacked a place...near Malakal and the SPLA (South Sudanese army) has repulsed them," Philip Aguer, SPLA spokesman, said.
Khartoum and Juba accuse each other of supporting rebel militias to destabilise their opponents, and each denies the other's charges.
The skirmishes have threatened to escalate into a full-blown conflict, which neither can afford. Most of the two nations' economically vital oil production has been shut down. Oil provides about 98 percent of South Sudan's state revenue, and Heglig accounts for half Sudan's 115,000 bpd output.
'No appetite for war'
The United States' special envoy to Sudan, Princeton Lyman, says neither Sudan nor South Sudan has "much of an appetite for war".
"Both their economies are suffering. Both their people are suffering. So, clearly, they have to get together for their own sakes to deal with several issues going on between them," he told Al Jazeera on Friday.
"When you talk to people behind the scenes, behind the rhetoric, neither side really wants to go back to all-out war. Neither side has the resources, [or] the will, to go into the kind of civil war they had before."
Lyman's comments came a day after the UN Security Council began talks on a draft resolution that would call for sanctions against Sudan and South Sudan if they fail to meet African Union (AU) demands to end their border war.
The draft resolution, circulated by the US on Thursday, backs previously stated AU demands that include withdrawing troops from the disputed border region, starting negotiations within two weeks, and opening humanitarian access.
"The intention of the text was to provide swift and substantive support to the decisions of the African Union, in the form that the African Union requested," said Susan Rice, US ambassador to the UN.
"But there were some members who either need more time to get guidance from their capitals or who are sceptical of the wisdom of going directly to a resolution."
The latest reports of fighting came as British aid group Oxfam said that tens of thousands of refugees in South Sudan's Jamam camp needed to be urgently moved to a new site to escape life-threatening water shortages and fatal diseases.
Alun McDonald, Oxfam's spokesperson, said the boreholes that provide the water for the camp in South Sudan's Upper Nile state can only serve 16,500 of the 37,000 refugees there.
Relief agencies also expect that more refugees fleeing the recent South Sudan and Sudan border conflict will be taking up residence in Jamam, he said.
South Sudan gained independence from Sudan in July after five decades of intermittent civil war.