Russian TV showed a huge crowd at the rally in Abkhazia
The separatist leaders of Georgia's breakaway regions of Abkhazia and South Ossetia have urged Russia to recognise their independence, at mass rallies.
Russian Foreign Minister Sergei Lavrov said Moscow's response to their pleas would depend on the conduct of Georgian President Mikhail Saakashvili.
Russia says it will keep troops in a security zone around South Ossetia.
It will extend several kilometres into Georgia proper. Russia also plans to strengthen its South Ossetia force.
"Tomorrow, eight checkpoints will be established in the security zone in which 500 peacekeepers will be deployed, no more than that," said Mr Lavrov, quoted by Reuters news agency.
It is still not clear to what extent Russian military forces have withdrawn from Georgia, despite Moscow's promise to pull out most of its troops by the end of Friday.
Russian news agencies say an armoured column, consisting of more than 40 vehicles, has passed through South Ossetia, on its way to the Russian border.
A BBC correspondent in the Georgian village of Igoeti, just 35km (21 miles) from the capital Tbilisi, said he saw the Russian military pulling back towards South Ossetia early on Thursday afternoon. Russian forces were also reported to be still dug in around Georgia's main Black Sea port of Poti.
Russia poured troops into Georgia after Georgian forces tried to retake South Ossetia on 7 August. Russian-led peacekeeping troops had been deployed there since a war in the early 1990s.
Russian troops moved far into Georgia from the breakaway regions
Thousands of people attended pro-independence rallies in the Abkhaz capital Sukhumi and war-ravaged South Ossetian capital Tskhinvali on Thursday.
The world-renowned conductor Valery Gergiyev - himself an Ossetian - plans to give a concert in South Ossetia with his St Petersburg orchestra on Thursday.
Chill in Nato-Russia ties
Meanwhile, Russia says it is reviewing its co-operation with Nato, which has insisted that Moscow pull its troops out of Georgia, in line with a French-brokered ceasefire agreement.
Nato said on Tuesday there could be no "business as usual" with Moscow.
At an emergency meeting, Nato suspended formal contacts with Russia because of the Russian military presence in Georgia.
"Relations with Nato will be reviewed," Russian Deputy Foreign Minister Alexander Grushko was quoted as saying by Interfax news agency on Thursday.
"This will apply to the military co-operation programme," he said.
Nato has accused Russia of failing to respect the truce, which requires both Russian and Georgian forces to pull back to the positions they held before heavy fighting erupted in South Ossetia.
On Wednesday, Norway's defence ministry said Russia had informed Norwegian diplomats that it was planning to freeze co-operation with Nato.
Norway's Aftenposten newspaper said Oslo was trying to establish exactly what impact the Russian decision would have on existing co-operation, such as joint rescue operations and border controls. Norway shares a border with Russia in the Arctic.
A statement from the Norwegian defence ministry said: "Norway notes that Russia has decided that for now it is 'freezing' all military co-operation with Nato and allied countries.
"We expect that this will not affect planned activities in the areas of coastguard operations, search and rescue and resource management, because on the Russian side these are handled by civilian authorities."
Russia has not yet given Norway formal written notification about its suspension of co-operation, a ministry spokesperson said.
Russia's permanent envoy at Nato headquarters in Brussels, Dmitry Rogozin, has been recalled to Moscow for consultations, Russia's Itar-Tass news agency reports.
He said that in light of Nato's position on the Georgia conflict, relations with Nato "really cannot remain as before", but he added that "there will not be a cold war".
A state secretary in Norway's defence ministry, Espen Barth Eide, said "there's no doubt that our relationship to Russia has now chilled".