At the core of this week's talks has been the issue of European security architecture.
Zelensky said he found the US approach of discussing a new European security order with Russia"a bit strange".
The territorial issue continues to be a key point of contention, Putin said.
Putin suggested a similar five-day ceasefire for Kostyantynivka, a contested front-line Ukrainian city in the eastern region of Donetsk.
Kyiv disputes that Russia fully holds Kostyantynivka, the town named in the ceasefire proposal.
The BBC reported that a truce could help Moscow's troops to make a final push to seize the town.
Zelensky said Ukraine was trying to clear up the Starlink situation with the American side.
Starlink, a satellite internet service, has come to play a vital role in facilitating communication on Ukraine's front line.