The European Union has said it is considering sending troops, while leaders of the Group of Eight meeting in St. Petersburg stressed on Monday that the force would have to have a mandate from the United Nations.
"The blunt reality is that this violence is not going to stop unless we create the conditions for the cessation of violence," Tony Blair, the British prime minister, said after talks with Kofi Annan, the UN secretary-general.
"The only way is if we have a deployment of international forces that can stop bombardment coming into Israel."
The prime minister's office said Blair was referring to an international force that would act as a buffer once hostilities had stopped.
Blair said he envisaged a force larger than the current UN force of some 2,000 troops which monitors the Blue Line separating Israel and Lebanon and is charged with reporting violations by either side.
US and Russia made compromises
on their positions on Middle East
Romano Prodi, the Italian prime minister, said Annan was looking to send approximately 8,000 more troops.
Vladimir Putin, the Russian president, said Moscow would decide whether to contribute troops only after the UN Security Council had endorsed the proposal, and Prodi said Italy was ready to contribute in a "significant way" if there were a Security Council mandate.
However Angela Merkel, the German chancellor, said sending troops was not on Germany's agenda.
Israel's initial reaction was cool. Prime Minister Ehud Olmert instead favours Lebanese forces taking control of the area of the border with Israel and wants the Hezbollah militia disarmed, senior Israeli officials said.
Olmert favours Lebanese forces
taking control of the border
Jacques Chirac, the French president, said it was essential to enforce UN Security Council Resolution 1559, which calls for the disarmament of Hezbollah and other militias in Lebanon. However, he cautioned that "some means of coercion" may be needed to enforce the resolution.
Putin, who had hoped to use the first G8 summit on Russian soil to burnish his country's standing on the global stage, saw his summit priorities overshadowed by the Middle East crisis.
But, after three days of talks, he said in a closing news conference that "all the aims which we had set ourselves have been achieved."
Following tough negotiations, the G8 issued a statement on Sunday blaming Hezbollah and Hamas for the escalating violence and recognising Israel's right to defend itself - although they called on the Jewish state to show restraint.
"For the first time, we've really begun to address with clarity the root causes of the conflict ... and that is terrorist activity - namely Hezbollah, that's housed and encouraged by Syria," Bush said - although there was no explicit referral to Syria in the G8 statement.
US, Russia compromise
Prodi said the eight leaders only managed to agree on the wording of the text because both the United States and Russia made compromises. The US position had strongly supported Israel's right to self-defence, while Russia held that Israel was engaging in excessive force.
"If you take Israel, the departure point was much more far away than the arrival point and both of them moved," Prodi said in English. "No one has lost. They remarkably moved."
"We were not guided by diametrically opposing objectives," Putin commented at his concluding news conference. "The objectives were common. At issue was to find correct and balanced language to reflect our concerns and positions."
The G8 - the United States, Russia, Japan, Germany, Britain, France, Italy and Canada – also called on North Korea to put a stop to its missile tests and to abandon its nuclear weapons program.
G8 leaders warned N Korea and Iran
against their nuclear ambitions
On Iran's nuclear ambitions, they sought to keep up pressure for a UN resolution seeking sanctions. "Iran has a serious choice to make and we invited it to make the right decision - to react positively to the concrete proposals presented to it," the leaders said.
The G8 leaders also met on Monday with seven leaders of developing countries, including the emerging economic powerhouses of China, India and Brazil for talks focused on restarting stalled global trade talks and implementing a major debt relief programme for the world's poorest nations, that was announced at last year's summit.