After the fourth round of bilateral negotiations held between Tuesday and Thursday in Moscow came to an end, the two sides agreed to resume the discussion on 13 May in the same city, reports YonhapNewsAgency.
"During the talks, both sides narrowed significantly their differences on the quota for Korean fishing boats, but Russia's circumstances desisted them from signing a pact on the quota," a source said.
The two countries agreed to set South Korea's fishing quota for cod, squid and mackerel pike for this year at the same level as last year, it said.
They also came to a settlement concerning pollack where Russia will permit South Korean fishing boats to catch up to 20,500 tons of the fish, which is half of last year's allotment, and then allow them to catch the remaining 19,500 tons when certain conditions are met, the source said.
Russia reportedly has taken the stance that it will allow South Korea to catch the rest of the pollack quota once South Korea takes concrete measures to prevent Russian crabs from being illegally traded in Seoul.
Russia's fisheries authorities have called on South Korea to map out measures to prevent illegally-caught Russian crabs from reaching the country via Japan.
Representatives from South Korea called for Russia to allow its fishing boats to fill its pollack quota, saying the Korean government has submitted to parliament a bill on the prevention of illegal trading of Russian crabs, the source said.
However, Russia's delegates remained firm stating that South Korean fishing boats could catch the additional pollack once the bill takes effect, the source said.
The two countries launched the talks in November, 2012.