BBC
Mr Kerry said he was committed to working with Moscow to ease the crisis.
Russia's Sergei Lavrov refused to meet his Ukrainian counterpart, whose government Moscow does not recognise.
A tense stand-off continues between pro-Russian forces and the Ukrainian military in the Crimea region, where a UN diplomat was threatened by gunmen.
Moscow has flooded troops into the Russian-dominated
Ukrainian region of Crimea in recent days, a move condemned by the West
as an illegal use of force.
'Zero expectations'
Mr Kerry met Mr Lavrov and counterparts from the UK, Germany and France on the sidelines of a long-planned conference on Lebanon in Paris.
In a news conference afterwards, the US foreign policy chief repeated that Russia's violation of Ukrainian sovereignty "would not go unanswered".
The talks ended with no firm deal, and without a direct meeting between Mr Lavrov and Ukrainian Foreign Minister Andriy Deshchytsia.
Some Ukrainian warships remain blockaded off the Crimean coast
John Kerry said the US position over the crisis had not changed one bit
Pro-Russian demonstrators were out in force once again in parts of Crimea and eastern Ukraine
Mr Deshchytsia is part of the new regime in Kiev, which came to
power after pro-Russian President Viktor Yanukovych fled to Russia.
Mr Kerry said he had had "zero expectations" that Ukraine and Russia would meet face-to-face in Paris.
Diplomatic sources told the BBC that the Russians and Ukrainians would spend the next few days "gauging domestic responses" before resuming talks.
The BBC's diplomatic correspondent Bridget Kendall says that the harsh rhetoric may still not go away but there is now a sense that - perhaps - a dialogue is possible.
In the Crimea region on Wednesday, pro-Russian forces continued their blockade of Ukrainian military installations.
Moscow has denied that their soldiers are involved in the
blockades, but some of the men have told the BBC that they are Russian
military.
In the eastern city of Donetsk, hundreds of pro-Russian protesters stormed again stormed the local government building just hours after being forced out.
The US has announced that it will boost its military co-operation with Poland and the Baltic states, after Warsaw expressed concern about long-term instability in the region.
And Nato chief Anders Fogh Rasmussen said he would be conducting a "full review" of his organisation's co-operation with Russia.
US Secretary of State
John Kerry has described a meeting with his Russian counterpart over
Ukraine as "tough", but promised to continue talking.
Russia's Sergei Lavrov refused to meet his Ukrainian counterpart, whose government Moscow does not recognise.
A tense stand-off continues between pro-Russian forces and the Ukrainian military in the Crimea region, where a UN diplomat was threatened by gunmen.
Continue reading the main story
Expectations were low on the part of Western diplomats that
these Paris talks could turn a corner. And in concrete terms, there was
no breakthrough.
Sergei Lavrov refused to allow the new Ukrainian foreign minister to join the talks, but he did hold a series of intense discussions with his EU counterparts and John Kerry, and they have all agreed to keep talking. Afterwards, Mr Kerry was cautious but positive. It had been a long and difficult day of negotiations, he said. But he did now have something to take back to President Obama.
It doesn't mean that the harsh rhetoric will go away. EU leaders on Thursday will continue discussions on ramping up sanctions. But there is now a sense that - perhaps - a dialogue is possible.
Analysis
Sergei Lavrov refused to allow the new Ukrainian foreign minister to join the talks, but he did hold a series of intense discussions with his EU counterparts and John Kerry, and they have all agreed to keep talking. Afterwards, Mr Kerry was cautious but positive. It had been a long and difficult day of negotiations, he said. But he did now have something to take back to President Obama.
It doesn't mean that the harsh rhetoric will go away. EU leaders on Thursday will continue discussions on ramping up sanctions. But there is now a sense that - perhaps - a dialogue is possible.
Robert Serry, the
secretary-general's envoy to Crimea, was forced to leave Ukraine after
being besieged by an angry mob chanting pro-Russia slogans.
'Zero expectations'
Mr Kerry met Mr Lavrov and counterparts from the UK, Germany and France on the sidelines of a long-planned conference on Lebanon in Paris.
In a news conference afterwards, the US foreign policy chief repeated that Russia's violation of Ukrainian sovereignty "would not go unanswered".
The talks ended with no firm deal, and without a direct meeting between Mr Lavrov and Ukrainian Foreign Minister Andriy Deshchytsia.
Some Ukrainian warships remain blockaded off the Crimean coast
John Kerry said the US position over the crisis had not changed one bit
Pro-Russian demonstrators were out in force once again in parts of Crimea and eastern Ukraine
Continue reading the main story
“Start Quote
Many at the Lenin statue were old and not well-off. Some, quixotically, waved the red flag of the Soviet Union”
Moscow regards the new government as illegitimate, and says that Mr Yanukovych is still the rightful leader.
Diplomatic sources told the BBC that the Russians and Ukrainians would spend the next few days "gauging domestic responses" before resuming talks.
The BBC's diplomatic correspondent Bridget Kendall says that the harsh rhetoric may still not go away but there is now a sense that - perhaps - a dialogue is possible.
John Kerry: Russia's violations have united the world behind the Ukrainian people
In the eastern city of Donetsk, hundreds of pro-Russian protesters stormed again stormed the local government building just hours after being forced out.
The US has announced that it will boost its military co-operation with Poland and the Baltic states, after Warsaw expressed concern about long-term instability in the region.
And Nato chief Anders Fogh Rasmussen said he would be conducting a "full review" of his organisation's co-operation with Russia.
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