UN estimates that some 1,200 internally displaced people live in a village near where the fighting broke out on Tuesday.
"While some people have been able to escape the fighting, many are unable to move to safer locations," said Martin Nesirky, spokesperson for UN Secretary General Ban Ki-moon, citing Nigam's call for a safe passage.
Nesirky added that due to the renewed fighting, UN and its partners had to cancel a mission last month to deliver assistance to people living in the area.
UN suspended assistance mission last month due to fighting
Nigam has called for immediate access for humanitarian partners, "as people are in urgent need of assistance," he said.
Government forces of Myanmar and the Kachin Independence Army, the army of Kachin Independence Organization (KIO) have been engaged in continuous fighting since June 2011 when a 1994 ceasefire agreement was broken. Since December 2011, the Myanmar government and KIO have held several rounds of peace talks.