Senior diplomats are meeting at the UN in New York amid signs that a deal on a resolution to end the violence in Lebanon and Israel is close.
Israeli jets targeted several Beirut suburbs on Friday morning
US Secretary of State Condoleezza Rice is among foreign ministers seeking to overcome differences on a draft text.
But Russia is now pushing its own plan for a three-day humanitarian truce - described by the US as "unhelpful".
Israeli air strikes have continued over Lebanon, while Hezbollah has fired a salvo of rockets into northern Israel.
The UN's Human Rights Council, meanwhile, has voted for an inquiry into Israeli attacks on civilians in Lebanon.
The council approved the resolution, brought by Islamic countries, by 27 votes to 11.
Eleven countries - many of which criticised the proposal for not condemning Hezbollah as well - voted against the move, while eight abstained.
Addressing the emergency session, the UN's human rights chief, Louise Arbour, chided both sides for inflicting suffering on civilians.
"Israeli attacks affecting civilians continue unabated," she told a special session of the UN Human Rights Council.
"Also unrelenting is Hezbollah's indiscriminate shelling of densely populated centres in northern Israel," she said, warning that commanders on both sides could face prosecution for war crimes and crimes against humanity.
At least 11 civilians were killed and 18 injured on Friday when Israeli jets attacked a bridge in Akkar province near the Syrian border, Lebanese hospital officials said.
Israeli jets also struck a vehicle near the eastern city of Baalbek, killing one person, according to medical sources.
Suburbs in the south of the Lebanese capital, Beirut, were also hit but there were no immediate reports of casualties.
Friday morning also saw Hezbollah fire several rockets into Israel. Several people were lightly injured in the port city of Haifa, Israeli medical sources said.
Fighting has also been continuing between Israeli forces and Hezbollah guerrillas near the Israeli border in southern Lebanon.
The Israeli army said a soldier was killed in fierce clashes in the western village of Labuneh, and 19 soldiers were injured across southern Lebanon overnight.
The Israeli military also confirmed the death of a soldier near Marjayoun - a mostly Christian town about 8km (five miles) from the border which Israeli troops overran on Thursday.
Troops from the UN peacekeeping force, Unifil, have gone to Marjayoun to evacuate some 350 Lebanese soldiers and police from the local barracks under an agreement with the Israelis, Lebanese officials said.
Despite the fighting, Israel says plans approved on Wednesday for a much deeper ground assault in south Lebanon are on hold to give diplomacy a chance.
European Union foreign policy chief Javier Solana is due in Beirut later on Friday for talks with the Lebanese Prime Minister, Fouad Siniora.
And US Middle East envoy David Welch has made a surprise return to Lebanon for talks.
The diplomatic focus is set to switch to New York later in the day as UN Security Council members make further attempts to agree on a draft resolution aimed at ending the fighting.
As well as Ms Rice, who arrived in New York on Friday morning, French Foreign Minister Philippe Douste-Blazy is also expected at UN headquarters.
UK Foreign Secretary Margaret Beckett is also in New York, saying she would "reinforce Britain's efforts to reach agreement".
Lebanon demands an immediate ceasefire and a quick Israeli withdrawal.
Israel says it will fight until new foreign troops and the Lebanese army move in - a position which Washington has supported.
As discussions continued, Russia said it was introducing its own draft resolution calling for a three-day truce for humanitarian purposes.
"War is raging in Lebanon and the humanitarian situation is getting catastrophic," Russian ambassador to the UN Vitaly Churkin said.
Russia's idea was rejected by Israel and described by the US ambassador to the UN, John Bolton, as "unhelpful".
More than 1,000 Lebanese, most of them civilians, have now been killed since the conflict erupted, Lebanon says. Some 123 Israelis, most of them soldiers, have also been killed.