Iakobashvili, minister for the reintegration of Georgia's breakaway regions, said that Georgia has "shown restraint and we will show restraint".
Jonah Hull, Al Jazeera's correspondent in Moscow, said: "I think Russia is playing the situation for its own interests and Georgia to a large extent is doing the same thing.
"I'm not sure this is an entirely accurate reading of the situation on the ground that these two sides are very close to war.
"Russia has an interest in perpetuating instability in the region... in order to derail Georgia's determined efforts to join Nato.
"Georgia is going to the international community, the European Union and Nato... and saying this is the kind of aggression we need protection from. I think it is significant these comments were made not in Tbilisi but Brussels."
Georgia has angered Russia, its former Soviet ruler, with which it shares a land border, by seeking Nato membership.
An April summit of the military alliance stopped short of giving it a definite track towards membership, but said it would be allowed to enter at a future date.
After the summit, Moscow announced plans to establish legal links with Abkhazia and South Ossetia.
The two areas broke from Tbilisi's control in the 1990s, seeking independence or absorption into Russia.
Tensions escalated after Georgia accused Russia of shooting down one of its drones over Abkhazia in April, a claim Russia denied.
Following Moscow's allegations that Georgia was planning to invade Abkhazia, an extra Russian contingent of troops was despatched to the area last week.
Russia has not said how many troops it has sent, but it has indicated that the total would remain within the 3,000 limit allowed under a United Nations-brokered ceasefire agreement signed in 1994.
Diplomats expect the reinforcement to be of the order of 1,200.
Russian soldiers acting as peacekeepers already patrol areas between Georgian and Abkhazian forces but handing full military control of the breakaway province to the Kremlin would alarm both the Georgian government and its Nato allies.
On Tuesday, Sergei Shamba, the de facto foreign minister of Abkhazia, said the region was ready to hand over military control to Russia.
"Those 200 km, the distance between the Psou and the Inguri rivers, are all Abkhazia," he said.
"We agree to Russia taking this territory under its military control. In exchange, we will demand guarantees of our security."
Sergei Lavrov, Russia's foreign minister, said Moscow had not received an official request from Abkhazia for its military to take control of the region.
Nato and the EU have urged Russia to reverse its actions, saying that the deployment of extra troops would add to tensions.