It was the 11th round of closed-door negotiations between the two foes and Georgia's breakaway territories, South Ossetia and Abkhazia, under the mediation of the European Union, United Nations and Organisation for Security and Cooperation in Europe.
"The situation remains difficult and at times dangerous and this holds true also for zones which two years ago were not conflict zones," EU mediator Pierre Morel told reporters.
Moscow recognised the rebel regions as independent states after crushing a Georgian assault on South Ossetia in August 2008, a war that rekindled tensions between the Kremlin and the West.
Under a ceasefire agreement mediated by French President Nicolas Sarkozy, Russian President Dmitry Medvedev and President Mikheil Saakashvili signed a commitment not to use force.
But Russia's Grigory Karasin, deputy foreign minister, said on Tuesday that the 12 August and 8 September agreements did not go far enough to meet the security concerns of people in the Black Sea region of Abkhazia and mountain territory of South Ossetia.
"Our logic really is that they are not enough. We can't constantly refer to these agreements as a guarantee of peaceful, happy life in the region," Karasin told a Geneva news briefing.
"In Abkhazia and South Ossetia they very much want Georgia to undertake such obligations because people are still afraid of force, the return of this so-called single, one Georgian state."
But Georgia, backed by its ally the United States, demanded Russia meet unfulfilled commitments in the existing agreement.
Georgia considered the 12 August agreement as legally binding on both sides and Tbilisi was fully implementing it, according to Giorgi Bokeria, Georgia's first deputy foreign minister.
"This agreement also includes the commitment by Russian forces to withdraw from Georgia," Bokeria told a separate briefing.
"So if there is any new agreement, which we are ready to work on with the Russian Federation, it should comply with all of those points which already exist in the 12th of August agreement," he said.
The US delegation, led by Assistant Secretary of State Philip Gordon, said that the 12 August ceasefire agreement already established the sides' commitment to the non-use of force.
"Full implementation of that agreement - which we still await from the Russian Federation - would render an additional agreement unnecessary," a US statement said.
Another non-use of force agreement could improve the situation provided it met the concerns of all parties, included "meaningful implementation measures" and avoided "unnecessary politicisation" of status issues related to the rebel regions.
EU mediator Morel, referring to the non-use of force, said: "The co-chairs have been trying to work on points of possible convergence and on the way to overcome differences which are very substantial."
These related to the legal analysis of the commitments already undertaken and considerations linked to the status of some participants and the signatories of any future documents.
"We can't work miracles, we can't just by a stroke of the pen reduce the differences. But it's important that this central issue which is at the heart of the security considerations is more or less all the time on our agenda," Morel said.
The next round of talks is set for 27 July, mediators said.
(EurActiv with Reuters.)