Following the latest meeting of Russian and Ukrainian delegates, Ukraine's President Volodymyr Zelenskyy said Russia's demands were beginning to become "more realistic."
"Efforts are still needed, patience is needed," he said in an address to his nation. "Any war ends with an agreement."
"The meetings continue, and, I am informed, the positions during the negotiations already sound more realistic," he added. "But time is still needed for the decisions to be in the interests of Ukraine."
Russia claims that Ukraine has now agreed to discuss neutrality.
"Neutral status is now being seriously discussed along, of course, with security guarantees," said Russian Foreign Minister Sergey Lavrov. "Now this very thing is being discussed in negotiations - there are absolutely specific formulations which in my view are close to agreement."
Kremlin spokesman Dmitry Peskov said that any agreement would require Ukraine becoming a neutral state like Switzerland, a notion which has so far been dismissed by Ukraine.
"Ukraine is now in a direct state of war with Russia," said Ukrainian negotiator Mikhailo Podolyak. "Consequently, the model can only be 'Ukrainian' and only on legally verified security guarantees."
Amid the peace talks, Russia has continued its military onslaught on Ukraine. Over three million refugees have now fled the nation.
The capital of Kyiv was bombarded overnight and is preparing for what seems like an inevitable full scale assault by Russian troops.
