Clashes have broken out in oil-rich border areas between Sudan and South Sudan in what has been called the biggest confrontation since the countries split last July.
South Sudan President Salva Kiir said his forces had seized a key oil field - a claim denied by Sudan.
Sudan state radio says President Omar al-Bashir has put off next week's visit to South Sudan for a summit.
The countries fought a long civil war before the South seceded from Sudan.
The clashes were first reported late on Monday and continued for a second day on Tuesday.
Gideon Gatpan, information minister for South Sudan's Unity state, told the BBC a Sudanese plane dropped two bombs 35 kilometres from the town of Bentiu.
He said he had no reports of casualties, adding that he believed the real targets were the nearby oil fields inside South Sudan.
The vice-president of the Greater Nile Petroleum Operating Company, Chom Bol, said a further bomb had landed near a camp for his staff inside the Unity oil field - in the South.
But a Sudanese armed forces spokesman denied there had been an air raid, saying there had been no fighting so far on Tuesday.
The nations disagree over several issues, of which the biggest is oil.
The two leaders had been due to hold talks at next week's summit in Juba, which had been billed as sign of improved relations.
Mr Kiir reportedly said his army had repulsed a Sudanese assault, and then taken over the oil fields in the area of Heglig, which is claimed by both sides.
The BBC's James Copnall in Khartoum says an international security source claims there had been fighting in the oil fields and oil workers were being evacuated.
Our correspondent says it is clear that, despite appeals for calm from UN Secretary General Ban Ki-moon and others, tension between Sudan and South Sudan is still very high.
Sudanese officials blamed a rebel group from the western Darfur region - the Justice and Equality Movement - for taking advantage of the situation to attack the Heglig area. A Sudanese army spokesman denied there had been any fighting inside the oil fields.
A spokesman for the South Sudan army said the clashes were the biggest confrontation since independence.
The fighting prompted Mr Kiir to warn of war.
On Monday evening he said: "This morning the [Sudanese] air force came and bombed... areas in Unity state.
"After this intensive bombardment our forces.... were attacked by the [Sudan army] and militia."
Mr Kiir added: "It is a war that has been imposed on us again, but it is [Sudanese] who are looking for it."
The South also reported Khartoum had attacked the disputed areas of Jau and Pan Akuach, and Teshwin inside South Sudan.
Sudan's army spokesman, Sawarmi Khalid Saad, confirmed fighting in the border area of Sudan's South Kordofan state and the southern Unity state on Monday, without giving the exact locations.
When the South seceded, it took most of the former Sudan's oil fields but all the pipelines still flow north, to the export terminal in Port Sudan.
In January, South Sudan shut down all of its oil fields in a row over the fees Sudan demands to transit the oil.
South Sudan depends on oil sales for 98% of state revenues, but pledged not to restart production until a deal was reached.
Parts of the countries' common border also remain in dispute.
In February, the two states agreed to demarcate most of the border within three months, although this would exclude five disputed areas.
And the two countries agreed a framework agreement to give their citizens basic freedoms in both nations.
They agreed to allow citizens of the other state to live, work and own property on either side of the border, and travel between the two nations.
The UN says about 350,000 southerners have moved to South Sudan since October 2010, after decades living in the north, but some 700,000 southerners remain.