Olmert, addressing the Israeli parliament, said: "The terrorist organisations that we are fighting take their orders from the Tehran-Damascus axis of evil.
"This is a moment of truth for Israel. We will fight with all the strength we are capable of.
"We will strike anyone who would strike at us and any terrorist infrastructure, until Hezbollah and Hamas cease attacking us."
The prime minister said Israel was fighting to implement the will of the international community in the implementation of UN resolution 1559 and the release of its abducted soldiers.
UN resolution 1559, like its follow-up 1680, calls for the pull out of all foreign forces from Lebanon, the disbanding and disarmament of all militias and deployment of the Lebanese army on the Israeli border.
"We have had enough"
It was Olmert's first major address since fighting against Hezbollah began six days ago.
He said Israel had not picked a fight with Lebanon and Hezbollah, or with the Palestinian militant group Hamas in the Gaza Strip, but now that its forces had been engaged, they would not back down until they had achieved their goals.
Olmert said: "Our enemies have challenged the state of Israel's sovereignty and the peace of its citizens, first in the south and then on the northern border and deeper into the country.
"Israel hasn't asked for these confrontations. To the contrary, we did a lot to prevent them. But there are those who interpreted our desire for peace as a sign of weakness.
"Our enemies erred in thinking that our readiness for restraint was a sign of weakness. They were mistaken.
"We are fighting for what in every enlightened country seems to be the obvious, the right to a normal life.
"There are days in the life of a nation when it must look at reality and say, enough is enough. And I say to everyone, we have had enough."