TONY EASTLEY: The ceasefire in the Middle East appears to be holding, despite isolated clashes that have left at least six Hezbollah fighters dead. Israel says its soldiers were acting in self-defence. But the truce has opened the way for a new political battle in Israel, as the ABC's Emma Griffiths reports from Jerusalem.

EMMA GRIFFITHS: Just hours into the ceasefire, its fragile nature was tested. Israel's military revealed it had shot dead a Hezbollah militant and during the first day of the truce at least six members of the militant group were killed. Israel's soldiers were acting in self-defence, as military spokesman Captain Jacob Dulahl explains.

JACOB DULAHL: That's a perfect example of a defensive operation where Hezbollah troops came very, very close, armed Hezbollah men came very, very close to our troops, endangering them. And as a result, we shot at them. They… it's clear if they don't approach us, if they don't attack us, there's a ceasefire. If they want to attack us, we'll defend ourselves.

EMMA GRIFFITHS: But Israel has vowed to actively hunt down the leaders of the militant group. Prime Minister Ehud Olmert addressed an extraordinary session of the Knesset, telling the Israeli Parliament Hezbollah's leaders are still a target. "These people will not be left alone," he said. "We will continue pursuing them anywhere, all the time and we do not intend to apologise or ask anyone's permission."

Israel and Hezbollah are under intense international pressure to hold back. The UN Secretary-General Kofi Annan says if either side breaches the ceasefire, it will suffer at the hands of world public opinion.

KOFI ANNAN: I urge the parties to make every effort in the interests of the civilian population on both sides to continue and consolidate the cessation. I also urge them to move swiftly to convert it into a lasting ceasefire.

EMMA GRIFFITHS: In Israel, domestic opinion is also troubling the Government. Ehud Olmert has promised an investigation into the war as the public mood swings against him. Many Israelis have questioned the war's outcome and are sceptical about the ceasefire.

VOX POP 1: I think, truthfully, that it is just a way for Hezbollah to regroup and I'm sure this is what they're going to do.

EMMA GRIFFITHS: And if Hezbollah regroups, what should Israel do?

VOX POP 1: Unfortunately there's not much you can do than, you know, get in there again and do what it's been doing until now.

EMMA GRIFFITHS: Ehud Olmert has asked his critics to be patient, saying Israel's fight against terrorism will continue.