Bakradze said Georgia was offering to send some 120 troops to support the French contingent in Kabul, the Afghan capital, and 200 others to accompany the Dutch in the southern province of Uruzgan which has seen some of the worse violence in fighting against the Taliban.
He said the forces would be deployed without "caveats", referring to national restrictions on what tasks they may perform and where they will go, which Nato commanders say have hampered the 47,000-strong International Security Assistance Force.
The defence minister said some smaller units would also be deployed alongside US troops in Afghanistan.
A Georgian defence ministry source said the whole contingent, which is expected to deploy in late August or early September, could reach 500 troops.
To date, the ex-Soviet state's only contribution to Nato's Afghan force has been one doctor, but it has several hundred servicemen in Iraq as part of a US-led coalition.
Georgia hopes to be given a Membership Action Plan, the roadmap to eventual entry to Nato, at the alliance summit which starts on Wednesday.
It has support from the US and ex-communist Nato members in central Europe, but is facing resistance from up to seven or eight West European countries.
They argue that Nato cannot set the Caucasus nation on the path to membership until it has settled territorial disputes with Russian-backed separatists on its soil, and point to its heavy-handed suppression of opposition protests last year.
They further contend that the move would unnecessarily damage ties with Russia, which is already angry over the Western-backed secession of Kosovo from Moscow's ally Serbia.
Georgia offered a power-sharing deal to its breakaway Abkhazia region on Friday which went further than previous offers, but Abkhazia's foreign minister rejected it.