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The Israeli army said three Israeli soldiers were killed in fighting in the south. Hizbollah said it launched multiple rockets at Matzuva in northern Israel, and the Israeli army said five of its soldiers were wounded in cross-border fire.
Three weeks after the war erupted when Hizbollah seized two Israeli soldiers in a cross-border raid, Israel's security cabinet agreed to step up its offensive, entailing a ground sweep 6-7 km (4 miles) into Lebanon, a political source said.
"We have so far now about six efforts running inside Lebanon...brigade-size or even bigger than brigade-size efforts in each one of them," Israeli Brigadier General Shuki Shahur said. An Israeli brigade usually has at least 1,000 soldiers.
Lebanese security sources said Israeli soldiers had landed by helicopter near Baalbek in the eastern Bekaa valley as aircraft launched several strikes in the region. An Israeli army spokesman declined to comment.
Israel said it would resume full air strikes in Lebanon early on Wednesday at the end of a partial, 48-hour suspension.
Olmert, who has rejected calls for an immediate halt to hostilities, said he saw signs of movement toward a ceasefire and that Hizbollah had suffered heavy losses.
"We are at the beginning of a political process that in the end will bring a ceasefire under entirely different conditions than before," he said. Israel says it will not stop fighting until an international force is in place in southern Lebanon.
Israeli artillery shells crashed down on the border area around the Lebanese village of Aita al-Shaab, where Hizbollah said it had destroyed a tank in battles with Israeli troops.
The three Israeli soldiers killed in Aita al-Shaab were the first army deaths since Israel lost nine soldiers on July 26. Hizbollah said it had inflicted 35 casualties in house-to-house battles in the village, and its television station aired footage of captured equipment including blood-stained body armor.
Israel's justice minister said about 300 of an estimated 2,000 Hizbollah fighters had been killed so far, and the tourism minister later said 400 had been killed.
Hizbollah, which says it does not hide its dead and that it has many thousands more fighters, has announced 43 deaths in that period and said the Israeli statements were false.
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