Demonstrators were to form a human chain running through the Georgian capital Tbilisi and demonstrations were planned in major European cities, said lawmaker Papuna Davitaia of the ruling United National Movement, one of the event's organisers.
"We are expecting tens of thousands of people, I think there will be over 30,000 just in Tbilisi," he said. He said the rally would "show the world and Europe our unity."
Georgia is hoping EU leaders will agree on a tough response to Russia's August 8 incursion into Georgia, continued occupation of several parts of the country, and recognition of independence for two Moscow-backed separatist regions.
President Mikheil Saakashvili called for Georgians to turn out en masse for the rallies and said he expected support from Europe during the summit.
"I expect that Europe will support our territorial integrity and will say that it will never recognise these illegal actions," Saakashvili said in an address to the nation Sunday, according to a transcript on his website.
Saakashvili said that "Russia today is more isolated than it ever was during the existence of the Soviet Union" and that the rallies "will show the entire world how united our people are."
Deputy Foreign Minister Grigol Vashadze told reporters in Tbilisi that Georgia was expecting the EU to agree to "adequate measures" against Russia.
"The fact that an extraordinary summit is being held is already a huge sign," he said.
"I believe the measures that will be taken will be in accordance with the situation we have in Georgia. My expectations are that there will be adequate measures."
Georgian Foreign Minister Eka Tkeshelashvili warned of a "domino effect" in the Caucasus region and Ukraine after Russia moved troops into Georgia, and ruled out any talks with Moscow in the short term.
"Russia's military hostility against the small state of Georgia could have a domino effect in other countries of the region like Ukraine," Tkeshelashvili said Sunday after meeting with Turkish counterpart Ali Babacan in Istanbul.
Tkeshelashvili said Tbilisi would not talk to Moscow "for as long as the Russian Federation has not left Georgia and does not fully apply the ceasefire."
The rally was to begin at 3pm (1100 GMT) in Georgia, about the same time EU leaders were expected to begin examining their relations with Moscow in Brussels.
"Our main message is unity against Russian aggression," Davitaia said. "Today all of us, the whole of society, are united despite political or other views."
Huge billboards reading "Stop Russia" were being put up in Tbilisi on Sunday in advance of the event.
Advertisements for the rally have been running on Georgian television for days.
The ads, which show victims of Russia's bombing campaign against Georgia and footage of a previous rally that drew tens of thousands to the streets of Tbilisi, call for Georgians to protest "hand in hand" on Monday.
"We will defeat evil together! Georgia is ours!" a voiceover said during the ad.
Russian troops entered Georgia to push back a Georgian offensive to retake the rebel enclave of South Ossetia, which broke away from Tbilisi in the 1990s with Moscow's backing.
Russian troops continue to hold positions in Georgia, serving in what Moscow describes as a peacekeeping mission. Tbilisi has labelled them an occupation force.
Russia's recognition of South Ossetia and another breakaway region, Abkhazia, as independent drew condemnation from Tbilisi and many Western countries.