The Ukrainian delegation had arrived earlier in the day, while Russia's had come to the city on Wednesday.
Vladimir Medinsky, head of the Russian delegation, told reporters on Wednesday that discussions would focus on "issues related to a cease-fire and the need for a humanitarian corridor."
"We discussed our positions at our previous meetings. Russia put forward a number of initiatives related to an immediate cease-fire," he said.
The first round of talks between Russia and Ukraine was held on Monday, with no concrete results after discussions that lasted for about five hours.
Both sides, however, agreed to hold a second round of negotiations to achieve a cease-fire.
