"Tel Aviv or elsewhere, we were certain that we could reach any corner or spot in occupied Palestine and now we are certain that we can reach them."
Nasrallah also said that Syria had been willing to engage in last year's war.
However, he said: "Hezbollah did not see the interest in that, and that the Israelis took into account the Syrian preparation but did not act militarily on the front which may require Syrian advancement."
The full interview will be aired on Monday.
The UN peacekeeping force in south Lebanon was expanded as part of an August 14 truce between Israel and Hezbollah and says its mandate is to ensure the group does not have a military presence south of the Litani river.
Lebanese security and political sources said in May that Hezbollah had replenished its rocket arsenal and received improved anti-aircraft and anti-tank missiles from Iran via Syria.
Israel and the United States accuse Syria and Iran of arming, training and funding Hezbollah.
Syria and Iran say their support to the Shia faction is purely political.
The Beirut government says it has no proof of arms transfers from Syria since August.
Israel has complained about Hezbollah's resupply effort but analysts have said although the group has rearmed since last year's war it has little interest in provoking a new one.
Lebanon has deployed regular forces along the frontier as part of the ceasefire and the border has been largely quiet since then.