The south`s forces have been widely blamed for an attack Thursday on UN peacekeepers who were escorting about 200 troops from the north out of the flashpoint region as part of an accord to defuse tensions.
An unknown number of UN and north Sudan troops were wounded.
"The secretary general strongly condemns the attack against an UNMIS (United Nations Mission in Sudan) escort convoy," said his spokesman Martin Nesirky.
"The attack was not only a serious breach of agreements between the parties, but also a criminal act against the United Nations," Ban was quoted as saying.
"The secretary general calls on the parties to immediately investigate the incident and ensure those accountable are brought to justice."
Ban was also "very concerned" about reports of increased troop into Abyei on Friday and called on both sides to stick to peace accords under which all unauthorized forces were to be withdrawn from Abyei.
Sudan`s two armies traded angry accusations over the attack on Friday, when aerial bombing raids and artillery shelling were reported. The United States has called on the south Sudan government to account for the attack.
South Sudan is to formally break from the north on July 9 and Abyei`s future is the most sensitive of a raft of issues the two sides are struggling to agree on. Both claim Abyei. (*)