Gela Bezhuashvili, the Georgian foreign minister, met his Russian counterpart Sergei Lavrov and other foreign ministers from the region at the start of a two-day Black Sea Economic Cooperation Organisation summit on Wednesday.
"The current difficulties are surmountable," Bezhuashvili said ahead of the meeting, Interfax news agency reported.
"There have been tensions, but they can be resolved," he added.
Russia responded the brief arrest of the officers by cutting off transport ties, deporting hundreds of Georgian citizens, and cracking down on Georgian-owned businesses in the worst dispute between the two neighbours since the Georgia's 2003 revolution.
Mikheil Saakashvili, the US-educated opposition leader brought to power by the revolution, has sought to reduce Moscow's influence on his country and move towards Nato and European Union membership.
Bezhuashvili said he would also try to arrange a meeting between Vladimir Putin, the Russian president, and Saakashvili at a summit in Minsk later this month, Russian news agencies reported.
Relations collapsed after four
Russian officers were arrested
"We always welcome any dialogue ... but a single contact will not solve the problem," said Igor Ivanov, the head of Russia's security council, who is also due to meet Bezhuashvili.
Ivanov said the success of the talks would depend on Georgia, saying it was up to Tbilisi to solve a crisis it had caused.
On Tuesday, Merab Antadze, Georgia's minister for conflict settlement, who is to take part in the talks, said Georgia would also put forward a plan to settle conflicts with its two breakaway regions, Itar-Tass news agency reported.
Georgia has long been angered by what it sees as Russian support for Abkhazia and South Ossetia, while Moscow accuses Saakashvili of planning military action there.
South Ossetia accused Tbilisi of plotting to assassinate the region's leadership and said it killed four Georgia-linked "saboteurs" earlier in the day.
Bezhuashvili has dismissed the claim as "disinformation" and an attempt "to exacerbate the situation in the region."