The UN negotiated a truce on August 14 ending more than a month of fighting which cost about 1,400 lives.
Nearly 1,300 people, mostly civilians, were killed in Lebanon and killed 160 people mostly soldiers, were killed in Israel.
The resolution paves for a strengthened UN force which would eventually number 15,000.
The truce also secured the withdrawal of Israeli troops, the deployment of the Lebanese army and disarming of Hezbollah.
The ceasefire has now entered its second week and is facing a major test after each side charged the other of breaking the truce.
The Israeli military claims it has killed at least two fighters from the Shiite militant group Hezbollah.
Israeli military officials say troops in southern Lebanon spotted a group of three armed Hezbollah fighters who looked threatening.
The army says the soldiers opened fire on them but a spokesman insists the incident did not violate the UN ceasefire.
He maintains the troops "acted in legitimate self-defence".
Lebanese Prime Minister Fuad Siniora has protested against what he called Israeli violations of his country's air space.
Israel says it would not hesitate to act against alleged cross-border arms smuggling to Hezbollah from Syria.
The threat was made despite criticism by UN chief, Kofi Annan, of Israel’s raid in eastern Lebanon on Saturday.
UN force urgent: Bush
In Washington, US President George W Bush called for the rapid creation and deployment of an expanded UN force.
"The need is urgent," said Mr Bush, a staunch supporter of Israel.
Mr Bush warned Hezbollah would be disarmed only once a "security zone" is created along the volatile Lebanon-Israel border.
Mr Bush said there would be a fresh UN resolution giving "further instructions to the international force."
White House officials quickly warned that the President may have misspoken.
They could not confirm whether the US was planning to bring forward a new resolution.
US ambassador to the UN, John Bolton, later said there was as no firm plan to present a new resolution to the Security Council.
He made clear that deploying peacekeepers was the priority.
"I think the initial force can be deployed now but it's obviously closely linked and we want the disarming of Hezbollah to be accomplished rapidly," he said.
Delays continue
US troops will not join an international force and the United Nations is struggling to persuade European nations to take part.
The UN is due to get 3,500 peacekeepers on the ground by next Monday but has so far failed to reach a breakthrough.
In New York, UN delegates spoke with Bangladesh, Indonesia, Malaysia and Nepal, the few countries with firm commitments.
The UN had hoped to convene a formal meeting early this week on generating a peacekeeping force.
But it will now await the outcome of the European Union talks in Brussels on Wednesday.
So far, Belgium, Denmark, Finland, France, Germany, Greece, Italy, Lithuania, Portugal and Spain said they were willing.
But all of them fell short of the numbers the United Nations had sought.
Italian Prime Minister Romano Prodi has reportedly told UN chief Kofi Annan that Italy was "available to command the UN mission."
The offer appears to be conditional on a new UN resolution.
Mr Prodi said he wanted the Security Council to clarify the force's mandate -- something the UN has said should not be necessary.
France had offered to lead the force but pledged only 200 troops.
Potential contributors to the UN mission are believed to fear being dragged into renewed fighting.
Disarmament of the Shiite militia group, Hezbollah, which is backed by Iran and Syria, is another stumbling block.
Hezbollah defiant
In Tehran, Hezbollah's representative Abdullah Safieddin warned that the group would not disarm.
"There will not be a disarmament, the UN resolution has not demanded that," Safieddin told the Shargh newspaper.
However, Lebanon has warned it would punish any group violating the truce in an implicit warning to Hezbollah.
Israel has warned that it was preparing for the "next round" against the Shiite guerrillas.
But in a sign of potential peace moves with Lebanon, Israeli Prime Minister Ehud Olmert evoked the possibility of talks.
"If the Lebanese government continues this way and if prime minister Siniora continues with his efforts to bring about change in Lebanon, I have no doubt that negotiations" with Beirut would lead to formal relations, he said.
Massive damage bill
Israel’s 34 day assault on Lebanon destroyed much of the country’s infrastructure, homes, roads, bridges and power stations.
The cost of the month long bombardment is estimated at US$3.5 billion (A$4.61bn).
Lebanon practically remains cut off from the outside world by an air and sea blockade imposed in the first days of the war.
Mr Bush has announced that US reconstruction aid to Lebanon would be boosted to US$230 million (A$303m).
He made US$13.5 million (A$17.8m) available for humanitarian aid, such as refugee assistance, the White House said.
US urged to do more
In a statement, Saudi Arabia said “the United States and the international community must shoulder their responsibilities to bring an end to these Israeli practices."
During a visit to Beirut, Qatar Emir, Sheikh Hamad bin Khalifa al-Thani, said that the Lebanese people and the "resistance" had achieved the Arab world's first "victory" against Israel.
Lebanese hopes of quick aid from the Arab League were dashed however when the 22-member bloc said they were committed to helping reconstruction but delayed discussions until September.