Nasrallah said the group has an arsenal of thousands of rockets and missiles, some of which he said could reach anywhere in Israel.
Nisreen el-Shamayleh, Al Jazeera's correspondent in Beirut, said Nasrallah warned that Hezbollah was not just going to blast holes in the walls of the building, but was ready to completely destroy them.
"That indicated that Hezbollah is now militarily and technologically stronger than it was before, " she said.
While Nasrallah said his group does not want war, if it happens Hezbollah will strike deep in Israel.
Our correspondent said Nasrallah pointed out he did not like the new language being used among a certain small group in Lebanon.
"He said poeple are saying that the very existence of Hezbollah, without them even doing anything, is enough justification for Israel to attack Lebanon," she said.
"Nasrallah said that this language must stop because it provides Israel with an excuse to attack Lebanon."
During the 2006 fighting, Israel pounded Beirut's southern suburbs as well as mainly
Shia southern Lebanon where Hezbollah maintains a stronghold and from which Israel withdrew in 2000.
Israel also destroyed dozens of buildings, including Nasrallah's offices, and Israeli warplanes bombed Beirut's Rafik Hariri Airport.
Hezbollah fired about 4,000 rockets into Israel, but its retaliation deep inside Israel did not reach Tel Aviv.
The war killed around 1,200 people in Lebanon and 160 in Israel.
Syrian and Lebanese officials have accused Israel repeatedly in the past few weeks of pushing for a war in the region, against the backdrop of an Iranian nuclear programme Israel views as a threat to its very survival.
Binyamin Netanyahu, Israel's prime minister, speaking on a visit to Russia on Tuesday said "we are not planning any war", and accused Iran of stoking fears as Western powers weigh additional sanctions against it over its nuclear programme.