Kerry met with his Russian counterpart Sergei Lavrov ahead of talks with Putin in the Black Sea city at what a top US official said was "a critical moment" for Ukraine, with Washington looking to ensure the "next steps in concrete implementation" of the truce deal.
The top US diplomat also wanted to discuss the conflicts in Syria, Yemen and Libya as well as brief Putin on the state of the negotiations seeking to reach a potentially historic deal on curtailing Iran's nuclear programme.
Kerry and Lavrov laid wreaths at a World War II memorial to mark 70 years since the victory over Nazi Germany ahead of their meeting.
Ties between Moscow and Washington collapsed when Russia seized the southern Ukrainian peninsula of Crimea in early 2014 and buttressed separatists in eastern Ukraine.
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But after a year of tensions, signs are emerging that both Russia and the West may be ready to seek detente.
And on a host of global issues -- from the threat of Islamic militants in Iraq to the civil war in Syria where US-backed Syrian rebels are seeking to oust President Bashar al-Assad -- Washington aims to engage Moscow's help.
Kremlin spokesman Dmitry Peskov described the visit by Kerry as "extremely positive" and said that his talks with Putin would cover a wide range of topics, from US-Russian bilateral ties to other international "hot-button issues".
"Through dialogue we can search for a path towards some sort of normalisation of ties and closer coordination in solving international problems," Peskov was quoted as saying by Russian wires.
"But this is only possible through dialogue."
Putin has refused to budge on Ukraine, despite a ceasefire agreement re-negotiated in February in Minsk, but has signaled readiness to mend ties with Washington and Brussels as Russia chafes under biting Western sanctions.
But "we've also made clear that if there is more serious violations that the pressure will increase."
Kerry wanted to "get down to some of the efforts on the ground to implement Minsk, make it absolutely clear that that's what we want to see and we want to be helpful.