Hizbollah leader Sayyed Hassan Nasrallah vowed more attacks on Israel's cities if it did not end an offensive launched after the group captured two soldiers in a raid on July 12.
"Rice is returning to the region to try to impose her conditions on Lebanon again to serve her new Middle East project and to serve Israel," Nasrallah said in a televised address, as Rice made her second trip to Israel this week.
Rice, who dined with Israeli Prime Minister Ehud Olmert on Saturday evening, said she hoped for agreement on the main conditions for a cease-fire to be outlined in a UN resolution that could be tabled as early as Tuesday.
"I expect the discussions to be difficult, but there will have to be give and take," Rice told reporters.
"I assume and have every reason to believe that leadership on both the sides of this crisis would like to see it end." Rice and Olmert were not scheduled to brief the media after their dinner given the sensitive stage of negotiations.
At least 469 people, mostly civilians, have been killed in Lebanon in the conflict, and 51 Israelis have died.
In the latest fighting, an Israeli air strike killed a woman and six children in a house in the southern village of Nmeiriya, medics said. Another strike also wounded two Indian soldiers with the UN peacekeeping force in southern Lebanon.
Meanwhile, Israel's forces pulled out of the Hizbollah stronghold of Bint Jbeil, just across the border, that was scene of some of the fiercest fighting in the 18-day conflict.
Rice welcomed an agreement on Thursday by Hizbollah cabinet members in Lebanon to seek an immediate cease-fire that would include the disarming of militias, and praised Lebanese Prime Minister Fouad Siniora for persuading Hizbollah to agree.
Lebanon's Siniora, whom Rice will meet during her stay in the Middle East, argues that the main issues to be resolved include Israel's occupation of the disputed Shebaa Farms area, claimed by Lebanon, and its detention of Lebanese prisoners.
In a softening of Israel's position that could help Rice steer the sides towards a cease-fire, a senior Foreign Ministry official said Israel would not demand the immediate disarming of Hizbollah, although it still wants it disarmed eventually.
Hizbollah fired more than 90 rockets from southern Lebanon into northern Israel on Saturday, lightly wounding about a dozen people, the army and medics said. They have launched more than 1,500 rockets into Israel since the conflict started.