Russia and Ukraine resumed talks via video link on Monday morning.
The negotiations wrapped later in the day, and they were expected to start up again Tuesday.
An official taking part in the talks said Ukraine's objectives were to secure a cease-fire, the immediate withdrawal of Russian troops from Ukraine and security guarantees.
The discussions come after a Russian shelling attack on a residential building in Kyiv's Obolon district killed two civilians and injured three, according to Ukrainian authorities.