A first set of talks failed to get off the ground last month because of disagreements about whether representatives from South Ossetia and Abkhazia should take part.
Moscow insists that the administrations of Abkhazia and South Ossetia be present.
The talks are being mediated by the EU, United Nations and the organisation for security and co-operation in Europe (OSCE).
Morel said that both Georgia and Russia asked the talks' mediators to draw up proposals for preventing security incidents and settling disputes in the Caucasus.
The proposals are to be presented at the next session, scheduled for December 17-18 in Geneva.
In August, Russia sent troops into Georgia after Georgian government forces tried to retake South Ossetia, which had thrown off Georgian rule in 1991-92.
Since their five-day war ended there have been shootings and explosions along the new de facto border.
Both Georgia and South Ossetia blame each other for stoking conflict, but the mediators hope to use the talks to build confidence and ease problems such as conditions for refugees and continuing violence.
"We are working from the bottom up to work towards medium and long term strategies for stabilising the situation," Morel said.
Sergi Kapanadze of Georgia's foreign ministry, who took part in the talks, said: "There was no walk-out. We talked about substantive issues. The process is going forward."
Georgia is wary of anything that would amount to international recognition for the breakaway regions, but has insisted that regional representatives loyal to Tbilisi also take part in the talks.
The United States, which sees Georgia as a regional ally in the volatile Caucasus, also participated.