Ms Rice, speaking en route to Israel, said there must be no place for “terrorist groups” like Hezbollah to launch attacks from Lebanese territory.
She will be meeting Israeli Prime Minister Ehud Olmert and other leaders.
Israeli war planes have kept up attacks against southern Lebanon, as Hezbollah fired missiles at northern Israel.
At least 362 Lebanese, many of them civilians, have been killed during the conflict, which is now into its 13th day. Thirty-seven Israelis have been killed, about half of them civilians.
The Israeli offensive began after Hezbollah captured two Israeli soldiers in a cross-border raid on 12 July.
Lebanese ‘let down’
Israel has said it is prepared to accept a European peacekeeping force in southern Lebanon providing it is robust and has a strong mandate.
Prime Minister Ehud Olmert made the announcement on Sunday after his government met envoys from Germany, France and the UK.
On the plane from Washington to Israel, Ms Rice told reporters Hezbollah must no longer be allowed to “plunge Lebanon and the region into war”.
“It is very important to establish conditions under which a ceasefire can take place,” she said.
“It is important to have conditions that will make it also sustainable.”
The BBC’s Kim Ghattas, in Beirut, says Lebanon has felt let down by the international community because there has been no call for an unconditional ceasefire.
However, Lebanese Prime Minister Fouad Siniora has also said there would be no return to the status quo before the violence started. And he insisted the Lebanese government was trying to extend its authority over the whole of the country.
Israel, which pulled out of southern Lebanon in 2000, has vowed to destroy Hezbollah’s ability to launch rockets at its territory.
But Hezbollah leader Sheikh Hassan Nasrallah said an Israeli invasion of southern Lebanon would not succeed.
“Any Israeli incursion will not have political results unless it achieves any of the announced goals, most importantly to stop the bombardment of Zionist settlements,” he told As-Safir newspaper.
“I assure you that this will goal will not be achieved.”
The Israeli prime minister has been making his position clear ahead of Ms Rice’s visit, the BBC’s Crispin Thorold reports from Jerusalem.
Refugees from south Lebanon have been arriving in Sidon
Ehud Olmert’s requirements include the enforcement of UN resolution 1559, which calls for the disarming of militias in Lebanon.
But Jerusalem now says it also wants robust peacekeepers to take the place of Unifil, the largely toothless UN force in southern Lebanon, our correspondent says.
Mr Olmert said he was prepared to accept the deployment of European soldiers in southern Lebanon instead.
This could be a Nato force or a European Union one but the Israeli premier insists that any troops deployed must have combat experience.
They would have, he added, to control border crossings between Syria and Lebanon as well as supporting Lebanon’s own army.
The Israelis are hinting at a more realistic assessment of what they can achieve through the application of brute force alone, BBC diplomatic correspondent Paul Adams reports from Jerusalem.
Senior political sources have told the BBC the government does not think its military operation will complete the task of disarming Hezbollah, and it believes it needs another week or 10 days in which to operate.
Saudi Arabia has urged Washington to press for a ceasefire between Israel and Hezbollah.