US Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov are due to hold crucial talks to try to ease tensions over the Ukraine crisis.
The US accuses Moscow of deploying troops in Ukraine's Crimea region, describing it as an "act of aggression" - a claim denied by the Kremlin.
Despite the sharp differences, both sides have hinted they would prefer to start a dialogue.
Moscow remains in de facto control of Ukraine's southern autonomous region.
The tense stand-off continued overnight in Crimea, with reports that Russian forces have seized part of a Ukrainian missile defence unit.
And in the east Ukrainian city of Donetsk, the regional government building has been evacuated and the area cordoned off amid unconfirmed reports of a bomb scare.
Earlier this week tensions escalated over Russia's warnings that it could move beyond Crimea into eastern Ukraine to protect Russians and Russian-speakers there.
The move has triggered wide condemnation across the globe.
In another development, Nato and Russia will hold talks in Brussels.
Nato chief Anders Fogh Rasmussen earlier said Russia continued to "violate Ukraine's sovereignty and territorial integrity".
Have taken part in US-UK-Ukraine consultations on Budapest Memorandum. Strong unity there must be costs for Russia if they don't de-escalate
— William Hague (@WilliamJHague) March 5, 2014
Kerry and Lavrov are expected to meet on the sidelines of a long-planned conference on Lebanon in Paris.
But the gathering is now being seen above all as a chance to test the waters for a dialogue about Ukraine, says the BBC's diplomatic correspondent Bridget Kendall.
People watch news in Independence Square, Kiev, on 4 March 2014
Ukrainians gathered in Kiev's Independence Square to watch the latest news on a large television screen.
US Secretary of State John Kerry boards plane in Kiev on 4 March 2014
US Secretary of State boarded his plane in Kiev to Paris, where he will hold talks with Russia's Sergei Lavrov.
Russian Black Sea Fleet crane ship in Sevastopol harbour, Crimea, on 4 March 2014
The presence of Russian warships are visible from the harbour in the Crimean city of Sevastopol.
On Tuesday, President Obama held a telephone conversation with German Chancellor Angela Merkel to discuss his plan to de-escalate the crisis, White House officials said.
They said Obama's offer to Moscow envisaged the return of the Russian troops in Crimea back to the bases of Russia's Black Sea Fleet in the peninsula.
The plan - which Obama discussed with President Putin on Saturday - also calls for sending a group of international monitors to Ukraine to ensure the rights of ethnic Russians are protected.
And it encourages a direct dialogue between the government in Kiev and Moscow.
Key recent events
21 February - After months of protests, President Viktor Yanukovych signs a deal with opposition leaders to reduce his powers and hold early elections
22 February - Yanukovych goes missing; protesters walk unopposed into official buildings as police abandon posts; parliament votes to impeach the president and calls elections for 25 May
23-26 February - Parliament names speaker Olexander Turchynov as interim president and Arseniy Yatsenyuk as PM; an arrest warrant is issued for Yanukovych, who alleges a coup
27-28 February - Pro-Russian gunmen seize key buildings in Crimean capital, Simferopol
1 March - Russia's parliament approves the use of military force; armed men blockade Ukrainian bases in Crimea
4 March - Russian President Putin denies troop deployments; US Secretary of State John Kerry condemns Russian "act of aggression"; Russia test-fires a ballistic missile
The Kremlin has so far not publicly commented on the offer.
Both President Putin and Lavrov have said they want to see a government of national unity in Ukraine, with more representation for the Russian-speaking population in the east of the country.
In one hint of progress, Ukraine's new Prime Minister Arseniy Yatsenyuk said consultations had taken place between Russian and Ukrainian ministers. He described them as "quite sluggish".
Russia's President Vladimir Putin on Tuesday denied the heavily armed troops that have taken over key sites in Crimea were Russian.
He said they were "local self-defence forces" loyal to Moscow, protecting the bases from "nationalists" and "anti-Semites".
In his first public comments on the crisis, he said Russia reserved the right to act to protect Russian citizens and speakers anywhere in Ukraine, but said military action was "a last resort".
Lavrov told reporters on Wednesday, following talks in Spain, that Moscow could not order the "self-defence forces" to leave the sites because they were not Russian forces.
He said Russian troops from the Black Sea Fleet - which is based in Crimea - were in their normal positions.
Moscow has strongly condemned the recent change of government in Ukraine, which came after months of street protests, more than 90 deaths and the flight of ousted President Viktor Yanukovych, a Russian ally.
Speaking during a visit to the Ukrainian capital Kiev on Tuesday, Kerry said there was no indication at all that Russian citizens or Russian-speakers were in any danger in post-uprising Ukraine.
"It is clear that Russia has been working hard to create a pretext for being able to invade further," he said.
However, Putin's decision to end military exercises near Ukraine's border has been seen as encouraging by some analysts.
Moscow has tightened its grip over the Crimean peninsula after troops thought to be Russian or pro-Russian began taking control of strategic points on Saturday.
Troops are surrounding Ukrainian military bases and other installations, while two Ukrainian warships are reported to be blocked by a Russian ship in the port of Sevastopol.