"I call on all concerned to refrain from unilateral actions which could escalate tensions in the area," Ban Ki-moon was quoted by the Reuters as saying at a news conference.
6,000 members of the NATO-led international Kosovo Force (KFOR) are ready to prevent the eruption of violence.
Ban's appeal for calm came before an evening meeting of the U.N. Security Council on the issue of the border posts as requested by Serbia and Russia. Western diplomats on the council said the 15-nation body was unlikely to take any action, the Reuters reported.
NATO Secretary-General Anders Fogh Rasmussen visited Pristina on Thursday and called on both the local Albanians and Serbs to enable dialogue and alleviate tensions.
Rasmussen visited Pristina a few hours before KFOR was to cease controlling two border crossings on the Serbia-Kosovo border.
On Friday morning, mixed teams of the EU rule or law mission in Kosovo (EULEX) and Kosovo police and customs officers are to take over control of the two border crossings in northern Kosovo. Serbia's authorities and Serbs living in the north of Kosovo are strongly opposed to that plan.
Rasmussen did not reveal any details of what should happen on Friday, but noted that NATO was prepared for an appropriate response in case of incidents.
The night between Thursday and Friday was calm in Kosovo. Local Serbs blocked the border posts of Jarinje ad Brnjak.