"We'll continue tomorrow. A very difficult and viscous negotiation process. There are fundamental contradictions. But there is certainly room for compromise," Podolyak tweeted.
Talks resumed Tuesday, with both sides having signalled progress.
President Volodymyr Zelensky said that the Russians "have already begun to understand that they will not achieve anything by war" and called Monday's talks "pretty good".
Russian Foreign Minister Sergei Lavrov said Tuesday at a press conference that "talks are now continuing on giving Ukraine neutral military status, in the context of security guarantees for all participants in this process", as well as on "demilitarising Ukraine", Interfax news agency reported.
Lavrov is set to meet his Turkish counterpart Mevlut Cavusoglu in Moscow on Wednesday to discuss the Ukraine conflict, the Russian ministry said.