Russian Foreign Minister Sergei Lavrov has set out demands for a neutral and federal Ukraine, ahead of crisis talks with his US counterpart in Paris.
Sunday evening’s meeting with Secretary of State John Kerry was hastily arranged after President Vladimir Putin phoned Barack Obama on Friday.
Russia has annexed Crimea and there are reports of thousands of Russian troops massed close to Ukraine’s borders.
Mr Lavrov has categorically denied any plans for an invasion.
But he has stressed Moscow will protect the rights of ethnic Russians and Russian speakers, after pro-EU protests in Kiev led to the ousting of Ukraine’s President Viktor Yanukovych.
He had faced months of protests after pulling out of an association deal with Brussels.
Hours before the Paris talks were due to take place at the Russian ambassador’s residence, Mr Lavrov told Russian state TV that Ukraine should come up with a new constitution “providing for a federal structure” and neutrality.
Russian Foreign Minister Sergei Lavrov: “We have absolutely no intention of, or interest in, crossing Ukraine’s borders”
The Russian foreign minister said Moscow, the US and European Union should act as a support group for Kiev to begin a nationwide dialogue that did not involve the “armed radicals”. Moscow claims that fascists have taken power in Ukraine, jeopardising the safety of Russian speakers.
In an interview on Saturday, he said Russia had been deceived after being promised “there would be no movement of Nato military infrastructure closer to our borders”.
Nato’s outgoing Secretary-General Anders Fogh Rasmussen warned on Sunday that Russia’s government was “[flouting] the principle that every state is sovereign and free to choose its own fate”.
Mr Putin is also thought to be demanding that Washington accepts Crimea’s independence from Ukraine.
Separately, Moscow is keen to tackle the issue of Trans-Dniester, a pro-Russian separatist region of Moldova on the south-western border of Ukraine. It accuses Ukraine and Moldova of “blockading” the area while the EU and the US stay silent.
US officials are divided over whether Mr Putin is seeking to ease tensions or is still planning further military action, BBC Paris correspondent Christian Fraser reports.
The Pentagon believes Moscow has massed tens of thousands of troops close to Ukraine’s eastern border.
Food, medicines and a field hospital are said to be among the supplies moved into position, officials say, which would not be necessary for any spring military exercise.
UK Defence Secretary Philip Hammond told the BBC: “Everybody is concerned. We are concerned that there might be a further incursion in the territory of a sovereign nation.”
The diplomatic push was initiated by President Putin, who spoke to President Obama for an hour late on Friday.
The next day, the US secretary of state abruptly diverted his flight from Saudi Arabia to Paris for Sunday’s meeting. “We are getting closer in our positions,” Mr Lavrov said on Saturday.
The White House, in its statement after Mr Putin’s phone-call, said President Obama made clear that a de-escalation of the crisis could only take place “if Russia pulls back its troops and does not take any steps to further violate Ukraine’s territorial integrity and sovereignty”.
People in the Crimean capital Simferopol have been celebrating the change of the clocks to synchronise with the time in Moscow
As the rest of Europe put clocks forward by one hour on Sunday, Crimea aligned its time with Moscow, jumping two hours ahead. Hundreds of people waving flags greeted the time change in the capital, Simferopol.
Voters in the mainly pro-Russian peninsula backed leaving Ukraine for Russia in a referendum a fortnight ago. But the vote has been condemned as illegal by Kiev and the UN General Assembly.