Discussions took place in Belarus, which has been assisting the Kremlin's invasion of its neighbour, and were led by Russian President Vladimir Putin's adviser Vladimir Medinsky.
Mr Medinsky said both parties' "positions are absolutely clear, they are written down point by point", including issues related to a political settlement of the conflict.
He added without elaboration that "mutual understanding was found on part of them".
Ukrainian presidential adviser Mykhailo Podolyak said the talks were unable to broker peace, but did offer hopes of "humanitarian corridors" to allow civilians to flee areas of fighting.
Both parties confirmed a third round of talks would be held soon.
Mr Putin used a televised address on Thursday to claim his military has offered safe corridors, so civilians can escape the war - which he has blamed on Ukraine.
The Russian leader made a series of statements which did not resemble what has been happening on the ground in Ukraine, including repeating his claim that his troops are fighting "neo-Nazis".
Putin vows to attack Ukraine 'until the end'
Ahead of his TV appearance, he used a call with French President Emmanuel Macron to say he was determined to press on with his attack "until the end".
Mr Macron said in a tweet: "I spoke to President Putin this morning.
"He refuses to stop his attacks on Ukraine at this point. It is vital to maintain dialogue to avoid human tragedy.
"I will continue my efforts and contacts. We must avoid the worst."
Zelenskyy's appeal: 'I don't bite'
Ukrainian President Volodymyr Zelenskyy has asked his Russian counterpart for face-to-face talks
Appealing to Mr Putin during a news conference, he said: "I don't bite."
Mr Zelenskyy's call came as Russian forces continued to bombard cities across his country, while they also battle for control of Enerhodar, a crucial energy-producing city in the south of Ukraine.
Mayor Dmytro Orlov has urged people not to leave their homes and said Ukrainian forces were battling Russian troops on the city's outskirts.
What's the state of the Russian advance?
Moscow's advance on Ukraine's capital Kyiv in the north has apparently stalled over the past few days, with a huge armoured column outside the city at a standstill.
But Russian forces are launching missile and artillery attacks on civilian areas and are making progress elsewhere, indiscriminately striking residential buildings as they go.
They are making significant gains in the south in a bid to sever Ukraine's connection to the Black and Azov seas, which would deal a crippling blow to the country's economy.
It would allow Russia to build a land corridor stretching from its border, across Crimea, which has been occupied by Moscow's forces since 2014, and all the way west to Romania.
The Russians have already announced the capture of Kherson, making it the first major city to fall since the invasion began just over a week ago.
Heavy fighting continued on the outskirts of another strategic port, Mariupol, on the Azov Sea.
Electricity and phone service were largely down in the city, and homes and shops faced food and water shortages.
Without phone connections, medics did not know where to take the wounded.