Ukraine crisis: Kerry, Lavrov hold last

London (CNN) -- As a contentious referendum on the future of Ukraine's Crimean region looms, U.S. Secretary of State John Kerry and his Russian counterpart Sergey Lavrov are holding last-ditch talks Friday in London.

The two met four times last week in Europe and have been in daily phone contact since. But they have failed to reach common ground on how to solve the crisis over Crimea.

They are now meeting again at the residence of the U.S. ambassador to London, as the clock ticks down on efforts to find a diplomatic solution.

Going into the talks, Kerry said he looked forward to examining 'how to move forward together to resolve some of the differences between us.'

Lavrov, speaking through a translator, said he also was satisfied that they are meeting. 'This is a difficult situation we are in. Many events have happened and a lot of time has been lost, so now we have to think what can be done,' he said.

A Ukrainian soldier looks out of the window of a regional military building with a poster reading 'Ukraine's armed forces wait for you!' in Donetsk, Ukraine, on Thursday, March 13. Pro-Russian forces have taken control of Ukraine's autonomous Crimea region, prompting criticism from the West and Ukraine's interim government.

Photos: Crisis in Ukraine

Protesters face off in city of Donetsk

Ambassador: Russia doesn't want war

Crimea's pro-Russian government has scheduled a referendum Sunday in which residents of the Crimean Peninsula will vote whether to secede from Ukraine and join Russia, or to choose effective independence.

Ukraine's interim government in Kiev, as well as U.S. and European leaders, have warned that the vote is illegitimate.

Before the talks with Lavrov, Kerry met with UK Prime Minister David Cameron and Foreign Secretary William Hague at 10 Downing Street.

'We want to see Ukrainians and the Russians talking to each other. And if they don't, then there are going to have to be consequences,' Cameron said.

Kerry said U.S. President Barack Obama was very grateful for Europe's unity and strong position on Ukraine. Both Europe and the United States have warned Russia of potential sanctions if it continues its actions in Ukraine.

'Hopefully, we all hope that we don't get pushed into a place where we have to do all those things. But we'll see what happens,' Kerry said.

'Costs' for Russia

A senior State Department official told reporters ahead of Kerry's arrival that 'there will be costs' for Russia if the Crimea referendum goes ahead.

'Our analysis is that Russia has encouraged, aided and abetted this referendum process from day one and financed it,' the official said.

The United States has urged Russia to deescalate the situation by talking to the government in Kiev, pulling back Russian forces in Crimea to their barracks and allowing in international observers to ensure the rights of all ethnic groups are maintained.

Russia has said that it has the right to intervene in Ukraine to protect ethnic Russians from 'fascists' and nationalists. It denies that its forces are militarily involved in Crimea, despite evidence to the contrary.

Ukraine's interim Prime Minister Arseniy Yatsenyuk blasted what he called Russia's illegal 'military aggression' against his nation as he addressed the U.N. Security Council in New York on Thursday

But he also insisted that a peaceful resolution that ends with Kiev and Moscow becoming 'real partners' is still possible, and that he is 'convinced that Russians do not want war.'

Yatsenyuk added, 'We still believe that we have a chance to resolve these conflicts in a peaceful manner.'

Russian military drills

Ukrainian PM: We urge Russia to pull back

Voices on the Ukraine/Crimea referendum

See dramatic Ukraine confrontation

Yatsenyuk's remarks come as about 8,500 Russian troops staged snap military exercises not far from his nation's eastern border.

The United States is 'very concerned' about the drill and will be asking Lavrov what is meant by it, the senior State Department official said Thursday.

'This is the second time inside of a month that Russia has chosen to mass large amounts of force on short notice without much transparency around the eastern borders of Ukraine,' the official said. 'It certainly creates an environment of intimidation, it certainly is destabilizing.'

Ukraine has been simmering since last November, when protesters angry at the then-government -- in part for its president's move toward Russia and away from the European Union -- began hitting the streets. In February, after deadly clashes between security forces and demonstrators, President Viktor Yanukovych was ousted.

Rising tensions have centered on Crimea, an ethnic Russian-majority peninsula in the country's southeast where local officials have declared their allegiance to Russia and armed men have blockaded Ukrainian military sites.

Tensions also have spilled over into other parts of eastern Ukraine, such as Donetsk, where the regional health authority said a 22-year-old man was stabbed to death and at least 10 others were injured in clashes Thursday between pro-Ukrainian and pro-Russian protesters.

Russia's Foreign Ministry condemned the Donetsk violence, saying 'right-wing radical groups' had attacked a peaceful demonstration against the interim authorities in Kiev.

'The authorities in Kiev are not controlling the situation in the country,' a statement on its website said.

While the bloodshed has been limited so far, fears are growing that the crisis could turn into a full-scale military conflict.

Speaking after Yatsenyuk at the United Nations, Russian U.N. Ambassador Vitaly Churkin accused the West of having 'fanned the flames of unrest' in Ukraine, citing their officials' 'blatant interference,' which he said had contributed to Yanukovych's 'illegal' ouster.

Since then, Ukraine's pro-western government has exacerbated the crisis by clamping down on opposition and effectively 'splitting this country (into) two parts,' Churkin said.

As to Sunday's referendum, the ambassador said citizens there deserve the same right to self-determination as anyone. 'Why should the Crimeans be the exception?' he asked.

Western officials warn Moscow

Western officials, meanwhile, warned Thursday that Russia will face significant consequences unless it changes course in Crimea, with Obama pledging to 'stand with Ukraine.'

In a speech to the German parliament, German Chancellor Angela Merkel said that Sunday's secession referendum was unconstitutional and that Russia's presence in the Black Sea peninsula violates Ukraine's territorial integrity. She warned Putin that his actions would lead to 'catastrophe' for Ukraine.

'It would also change Russia economically and politically,' she said.

In a phone call, French President Francois Hollande told Putin the referendum 'has no legal basis,' urging the Russian leader to 'do everything to prevent the annexation of Crimea to Russia.'

At a Senate committee hearing in Washington, Kerry predicted that the upcoming vote would favor Crimea rejoining Russia.

But he warned that, absent movement by Russia toward negotiating with Ukraine on the crisis, 'there will be a very serious series of steps Monday in Europe and here.'

The U.S. Senate is weighing legislation that could impose economic penalties on Russians involved in the intervention in Crimea. The measure would represent some of the toughest sanctions on Moscow since the end of the Cold War.

Last week, Obama issued an executive order slapping visa bans on Russian and Ukrainian officials involved in the intervention and laying the groundwork for financial sanctions against those responsible for the crisis.

The European Union has been divided over how quick and severe the sanctions should be, but European officials say they are considering travel bans, asset freezes, and possibly sanctions against Russian companies and banks if Russian aggression continues.

A way out for Putin?

American historian Timothy Snyder, author of 'Bloodlands: Europe between Hitler and Stalin,' said Putin has put himself in a difficult position, but there may still be an exit route.

'All of the official claims that have been made by Russia have been met. Their bases are secure, Russian speakers are not under any threat -- so there is in theory a way out for the Russians, since none of their reasons for intervention are actually true,' he said.

But the blitz by the Russian 'propaganda machine' may make it harder for Putin to scale back Russia's activities, he said, with many Russians believing the claims made of a serious fascist threat to Russian speakers in Ukraine.

'Putin has now put himself in a very exposed position, has staked his leadership and his popularity on some kind of victory here, so it seems that he has unleashed a process that is now beyond his control,' he said.

Alexander Nekrassov, a former Kremlin adviser, offered a very different take on events. He told CNN's Christiane Amanpour that Putin had no choice but to intervene after what Nekrassov said was 'basically an armed coup' in Kiev.

'The situation got out of control,' he said. 'There was no way Russia could afford to have a sort of a semi-simmering civil war in Ukraine. The situation in Crimea -- there would have been a bloodbath there, there would've been -- there was no choice for Putin, and he had to act.'

Nekrassov said there was no question that the referendum would go ahead Sunday, despite the efforts of U.S. and EU leaders to halt it.

CNN's Yon Pomrenze, Greg Botelho and Marie-Louise Gumuchian contributed to this report.