In a statement released by Ban's spokesperson on Sunday night, he said, "The ceasefire appears to be largely holding, giving a desperately needed respite to civilians trapped in the area and contributing to a swift and peaceful resolution of the conflict," Xinhua reported.
The nations such as Russia, Ukraine, France and Germany announced a peace deal following 14-hour marathon talks in Minsk, Belarus on Thursday.
The deal envisages a ceasefire between Ukrainian forces and independence-seeking insurgents starting on Sunday, followed by the withdrawal of heavy weapons from the frontline and constitutional reform to give eastern Ukraine more autonomy.
"However, the Secretary-General is seriously concerned over reports of continued instances of hostilities including in Debaltseve and reiterates his call for all parties to abide by the ceasefire without exception," the statement said.
Hostilities between government troops and pro-independence rebels in eastern Ukraine flared up with new vigour after the deal was announced.
The surge in fighting came as the warring sides accused each other of pushing an offensive to make territorial gains before the ceasefire was scheduled to take effect.
Ukrainian Deputy Defence Minister Petro Mekhed said the rebel forces were aiming to capture the government-controlled Mariupol and Debaltseve towns before the ceasefire deal came into force.