Relations between Tbilisi and Moscow are deeply strained over the fate of two regions of Georgia, South Ossetia and Abkhazia, that are seeking independence or incorporation into Russia.
Officials say the Russian man was arrested in 2006 in a sting operation by Georgian agents, but that the case was not publicized by Georgia until this week.
Lavrov's criticism of Tbilisi came on January 26.
The source of the uranium has not been confirmed.
But AP reported today that the suspect initially investigators that the material came from the Siberian city of Novosibirsk but that he later retracted that claim.
A Georgian official quoted by AP suggested that Moscow has been uncooperative in the probe, although the agency said Russian authorities countered that they were provided too small a sample of the material to determine its origin.
Highly enriched uranium, in sufficient quantities, could be used to make a nuclear bomb.
The spat between Georgia and Russia has extended to trade, diplomatic, and visa disputes.
Tbilisi has withdrawn its bilateral backing of Russian membership of the World Trade Organization (WTO), and set strict conditions on Moscow for its support.