Speaking after talks with Alexander Stubb, his Finnish counterpart, Lavrov sharply criticised the West for what he said was its failure to try to persuade Tbilisi to renounce force while condemning Moscow.
"Our foreign partners have done nothing to force Tbilisi, to use their influence with Tbilisi, for the signature of a legally-binding document" on renunciation of force, he said.
Nicolas Sarkozy, president of France, which currently holds the rotating EU presidency, was due in Moscow on Tuesday to hold talks with Dmitry Medvedev, his Russian counterpart, on a plan to end the conflict.
But Vitaly Churkin, Russia's ambassador to the UN, on Monday rejected the proposed Western draft resolution in the Security Council based on a three-point French peace plan.
Sarkozy was also expected to travel to Tbilisi later in the day to meet Mikheil Saakashvili, Georgia's president.Gori bombardment
Al Jazeera's Alan Fisher said that Russian forces had taken up positions on the hills around Gori as their aircraft bombed the the town about 30km outside separatist South Ossetia.
|Gori has been under sustained bombardment from Russian forces [EPA]
"This has been going on, at least as far as the bombing is concerned, for about two hours. Sustained attacks at regular intervals dropping about 10 bombs every time they attack the town," he said from the edge of Gori.
"It seems now they have stopped bombing the centre of the town and are now concentrating on Georgian army positions on the outside, but the fact that they are actually bombing Gori would suggest that the Russian army had actually moved into the town."
Lado Gurgenidze, Georgia's prime minister, said in a televised statement that the central square of Gori had been hit and university buildings were on fire.
Georgia said on Monday that the country had been cut in half as Russian forces took control of the key town, but Moscow denied seizing the town.
Gori sits on Georgia's only east-west main road, from which Moscow could cut off eastern Georgia from the country's western Black Sea coast.
Alexander Lomaia, Georgia's national security council, secretary, said on Tuesday that Russian forces were bombing a residential area in Tkviavi, a village near Gori.
"There were almost no civilians there as they were evacuated previously," he said.
Meanwhile, Russian-backed separatist forces in Abkhazia launched a series of artillery strikes early on Tuesday, aimed at pushing Georgian troops out of the Kodori Gorge, the only part of the breakaway region Tbilisi still controls.
Russia's Itar-Tass news agency, citing the general staff of Abkhazia's armed forces, reported that a group of around 250 Georgian soldiers had been surrounded.
Russian forces also crossed into the towns of Senaki, Zugdidi and Kurga in western Georgia from Abkhazia, before returning later.
In South Ossetia, a spokeswoman for the separatist administration said that at least 12 people had been wounded as Georgia shelled the capital Tskhinvali overnight.
"Last night was relatively calm," Irina Gagloyeva was quoted by as saying by the Interfax news agency.
"However some small units fired on South Ossetian interior ministry and peacekeepers' posts. Georgian mobile batteries were active and the city was hit by howitzer fire four times."