UN Secretary General Ban Ki-moon has criticised South Sudan, saying its seizure of Heglig oil field in Sudan is illegal.
Mr Ban urged the south to withdraw its forces immediately to stop border clashes spiralling into a war.
South Sudan has issued a statement to say it is not interested in war with its northern neighbour.
It says Heglig is rightfully part of South Sudan and it does not want the north to use it as a base for attacks.
But Mr Ban said the seizure of Heglig "is an infringement on the sovereignty of Sudan and a clearly illegal act".
"I also call on the government of Sudan to immediately stop shelling and bombing South Sudanese territory and withdraw its forces from disputed territories," he added.
South Sudan says it will only withdraw from Heglig if the UN deploys monitors there.
In Sudan, President Omar al-Bashir continued his verbal attacks threatening to teach the south a "final lesson". On Wednesday he had threatened to bring its government down.
The BBC's James Copnall in Juba, South Sudan, says the next decisive step is likely to be Sudan's attempt to retake Heglig by force.
But diplomats are hoping this can be avoided.
The Arab League has scheduled an emergency meeting in Cairo next week to deal with the crisis.
There is deep distrust between the two Sudans. South Sudan gained independence last year but the two countries cannot agree on the position of the border.