Fighting has continued for a second day between Sudan and South Sudan in the disputed border regions.
The AU says it is deeply alarmed and called on both sides to exercise the utmost restraint.
Khartoum says it is withdrawing from negotiations with South Sudan and has complained to the UN and the AU about South Sudan’s “aggression”.
A military spokesman for South Sudan told the BBC his troops were coming under aerial bombardment north of Heglig.
The BBC’s James Copnall in Khartoum says that Sudan relies on the oilfield for a sizeable part of its budget.
Sudan has vowed to use “all legitimate means” to retake the oil fields, and has warned of “destruction” in the south.
The fighting is the most serious conflict between the neighbours since South Sudan seceded in July last year.
In January, land-locked South Sudan, which depends on oil sales for 98% of its revenue, shut down all of its oil fields in a row over the fees Sudan demands to transit the oil.
A presidential summit, which was to have been held in South Sudan’s capital, Juba, at the beginning of April, has been postponed indefinitely because of the recent violence.
A senior Sudanese official, Ibrahim Ghandour, says South Sudan’s actions mean reconciliation efforts are now off the agenda.
“We cannot talk about peace while there is an aggression,” he said. “If they want peace, they have to pull their forces from the territory of Sudan.”
But South Sudan’s military spokesman, Colonel Philip Aguer, says his forces are simply acting in self-defence.
“We pursued them up to Heglig,” he said. “We think this is our right.
“We have never aggressed anybody. We have never crossed into the territories of the Republic of Sudan.”
In a statement, the African Union called upon both countries to resolve this and all other outstanding issues “in a peaceful way in accordance with the overriding principle of establishing two viable states in Sudan and South Sudan”.
Correspondents say Sudan, having lost most of its oil when the south seceded, will not tolerate losing any more.