Israeli soldiers killed six Hizbollah fighters in four skirmishes in Lebanon after the UN-imposed ceasefire took effect on Monday, the army said. Israeli Prime Minister Ehud Olmert later said he took sole responsibility for the offensive, and acknowledged ‘‘deficiencies’’ in the way the war was conducted.

In Beirut Hizbollah leader Sheik Hassan Nasrallah said his guerrillas had achieved a ‘‘strategic, historic victory’’ against Israel, calling Monday ‘‘a great day.’’ He also promised Hizbollah would help the Lebanese people rebuild.

‘‘We are today before a strategic, historic victory, without exaggeration,’’ he said in a taped speech on Hizbollah’s al-Manar TV.

The developments came as Lebanese civilians defied an Israeli travel ban and streamed back to their homes in war-ravaged areas.

In an address to parliament, Olmert said the ceasefire agreement eliminated the ‘‘state within a state’’ run by Hizbollah and restored Lebanon’s sovereignty in the south. Defence Minister Amir Peretz said the war opened a window for negotiations with Lebanon and renewed talks with Palestinians.

But many Israelis were upset by the high casualties during 34 days of fighting, and Benjamin Netanyahu, head of the opposition Likud Party, told lawmakers there were many failures in the war.

For the first time in a month, no rockets were fired into northern Israel, but few Israelis who fled the war were seen returning, and Israel’s government advised them to stay away for now to see whether the truce held.

Officials said four Hizbollah guerrillas were killed in two clashes near the town of Hadatha when armed men approached Israeli troops three hours after the ceasefire began, at 8 am Israeli time. Later clashes occurred near the towns of Farun and Shama, with one guerrilla killed in each.

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