The letter follows a series of confrontations between peacekeepers and residents in southern Lebanon, a stronghold of the armed Shia political party Hezbollah which fought a bloody war with Israel in 2006.
The clashes are believed to have been sparked by rumours that Unifil has increased the number of patrols in the area while reducing co-operation with the Lebanese armed forces.
But in the letter, Cuevas insisted that this is not the case. "Unifil works in close co-operation with the Lebanese army and we ensure that all our activities are fully coordinated," he wrote.
"This co-ordination does not imply that every one of the 350 daily patrols that Unifil does can be physically accompanied by the Lebanese army."
Some Western diplomats have said they believe that Hezbollah is behind the recent unrest, but the group has denied any role in the confrontations.
The heightened tension comes as Israel continues to insist that the peacekeeping force is not doing enough to prevent the flow of arms to Hezbollah in the south of Lebanon.
The UN says that this is the role of Lebanese authorities.
On Wednesday, the Israeli military published an aerial photograph showing what it said were Hezbollah positions and weapons stores in the village of Khiam.
Since the end of hostilies in 2006, Hezbollah and Israel have engaged in a bitter war of words, with both sides accusing the other of violating the Security Council resolution that ended the fighting.
But despite this, and occasional exchanges of fire over the border, Israeli security officials say they do not believe another round of violence appears imminent.
In a report on the situation in southern Lebanon released last week, Ban Ki-moon, the UN secretary-general, said that Israeli claims that Hezbollah had taken delivery of Scud missiles via Syria had led to a rise in tension in the area.
The recent confrontations between Unifil and residents in southern Lebanon will be discussed, at France's request, at the UN Security Council on Friday.