Russian officials put the situation on the agenda of the G8 gathering in St Petersburg which starts today and runs to Monday.
Summit host President Vladimir Putin urged all sides to "immediately stop military action" and said he would discuss the crisis with US President George W. Bush in pre-summit bilateral talks and over the weekend with the other G8 leaders.
Mr Bush arrived in Mr Putin's home city for face-to-face talks before the annual summit, which also includes Britain, Canada, France, Germany, Italy and Japan.
But while European Union nations have called on Israel to keep its actions "proportionate," Mr Bush's remarks - echoed to an extent by Canada - have been more supportive of Washington's closest regional ally.
He has called for restraint from Israel, saying it has the right to defend itself but urging it not to undermine Lebanon's fragile government.
Washington separately vetoed a UN resolution demanding an end to the military operations in Gaza.
Russia has criticised Israel's "disproportionate use of force" against Lebanon and the Palestinian territories.
The rest of the G8 leaders arriving Saturday will find Saint Petersburg in lockdown security mode.
Airspace has been closed to commercial traffic until Monday, sea and river access has been blocked and air force jets are patrolling overhead, with thousands of extra security forces on the streets.
After his arrival in St Petersburg, Mr Bush laid a wreath at a World War II memorial and then met representatives of non-governmental organisations and human rights groups.
After vowing to raise worries on the pace of democratic reform in Russia, which has drawn a sharp response from Mr Putin, he voiced concern at the meeting over the fate of Mikhail Khodorkovsky, the jailed founder of the Russian oil group Yukos.
Later, Mr Bush and his wife Laura joined Mr Putin and his wife Lyudmila for a barbecue dinner at the refurbished Konstantin Palace.
Separately, US and Russian negotiators are working flat-out on a possible deal that would clear the way for Moscow to join the World Trade Organization, which sets global trade rules.
Energy-rich Russia is currently the only major power operating outside the WTO.
US Senate resolution
Meanwhile the US Senate has adopted a non-binding resolution denouncing Russian "authoritarianism" under President Putin's six-year rule.
"In the six years since President Putin took office, Russia has experienced the biggest rollback of freedom that's occurred anywhere in decades," said Democratic Senator Joseph Biden before the chamber adopted the resolution.
"It is time for leading democracies to recognise that fact, and get tough on the Putin administration's attempts to suppress political dissent and bully Russian neighbours."
The resolution criticised Mr Putin for drafting an "authoritarian government drawn from the ranks of the KGB" and warned Bush that Russia would become "our problem later" if the nuclear-armed power was not kept in check.