JERUSALEM, Aug. 29 — United Nations Secretary General Kofi Annan came to Israel late Tuesday after two intensive days in Lebanon that he said had convinced him the Lebanese were serious about preserving the cease-fire and moving to a permanent peace.

“They believe that, handled properly, they can use this moment to strengthen their state,” Mr. Annan said in an interview in his hotel room in Jerusalem.

The Lebanese were committed, he said, to “the idea that you cannot have a state within a state but have to have one authority, one law and one gun.” His reference was to the dominance in southern Lebanon of the Hezbollah militia, which provoked a hugely destructive 34-day war with Israel by capturing two Israeli soldiers on July 12.

“I believe the Lebanese because they have seen what has happened to their country,” he said.

Mr. Annan had spent his second day in Lebanon seeing much of that destruction on a tour of the border area in the south and a visit to the headquarters of Unifil, the 2,000-member United Nations force in Lebanon. The strength is soon to grow to 15,000, matched by a like number of Lebanese Army troops, to patrol the south.