Russia, the US and the EU say that all sides have agreed to steps to "de-escalate" the crisis in Ukraine at talks in Geneva.
The world's statesmen have long grappled with the diplomatic problems of Syria and Iran, but neither pose the dangers of the Ukraine crisis.
Ukraine's acting president launched an "anti-terrorist operation" against pro-Russia separatists in the eastern region.
Russian state television said five people have been killed in a gunfight near the eastern Ukrainian town of Slaviansk controlled by pro-Moscow separatists.
Ukraine's Prime Minister Arseny Yatseniuk has said he is concerned as to how far Russia's President Putin will go in what he called attempts to restore the Soviet Union.
"President Putin has a dream to restore the Soviet Union. And every day, he goes further and further. And God knows where is the final destination," Yatseniuk told NBC's Meet the Press for an interview that will air on Sunday morning.
He added: "And I believe that you do remember his famous Munich speech saying that the biggest disaster of the former century is the collapse of the Soviet Union. I consider that the biggest disaster of this century would be the restoring of the Soviet Union under the auspices of President Putin."
The Ukrainian prime minister also said that those behind an anti-Semitic leaflet in the eastern city of Donetsk earlier in the week will be held responsible.
A mediator from Europe's OSCE security body headed to eastern Ukraine seeking the surrender of pro-Russian separatists as the Kiev government declared an Easter truce following a peace accord with Moscow.
Gunmen occupying public buildings in Donetsk and other border towns refuse to recognise an accord in Geneva on Thursday by which Russia, Ukraine and Kiev's US and EU allies agreed that the OSCE should oversee the disarmament of militants.
Ertogrul Apakan, who heads the special mission in Kiev of the Organisation for Security and Cooperation in Europe, said his deputy would be in Donetsk and meet separatist leaders by Sunday to see if they will comply with the agreement.
Swiss envoy Christian Schoenenberger said: "For the time being the political will is not there to move out [...] That's the task of the monitors, to create this political will, inform the people, so eventually they will understand that the best option for them is to move out."
Ukraine's foreign ministry has said that the 'anti-terror operation' against pro-Russian separatists has been put on hold over Easter.
The SBU, Ukraine's state security service said the suspension was "linked to the implementation of the Geneva agreement and the Easter holidays".
The extra Russian military forces near the border with Ukraine have been deployed there in response to instability in Ukraine, a Kremlin spokesman said. This marks a departure from previous comments which explained their presence as routine exercises.
"We ... have forces in the region of the Ukrainian border. Some of these forces are based there permanently, others are there to reinforce, against the backdrop of what is happening in Ukraine itself," Dmitry Peskov, spokesman to Russian President Vladimir Putin.
"Forgive me but, it (Ukraine) is a country where there has just been a military coup, so naturally any country is going to take particular precautionary measures in terms of ensuring its security."
He denied allegations the Russian military was interfering in events inside Ukraine territory.
President Putin says Russia will award state medals to some Russian servicemen who are involved in the Crimea operation.
Speaking to Russian television Putin said that there was nothing to prevent the normalisation of relations between Russia and the west, but that it would depend on the west.
The White House has renewed President Obama's demands that the Kremlin use what Washington believes is its influence over the separatists in Ukraine to get them to vacate government buildings.
It warned of heavier economic sanctions than those already imposed over Crimea if Moscow failed to uphold the Geneva deal - or if it moved to send troops massed on the border into Ukraine.
"We believe that Russia has considerable influence over the actions of those who have been engaged in destabilising activities in eastern Ukraine," national security adviser Susan Rice said.
"If we don't see action commensurate with the commitments that Russia has made yesterday in Geneva ... then obviously we've been very clear that we and our European partners remain ready to impose additional costs on Russia.
"Those costs and sanctions could include targeting very significant sectors of the Russian economy."
President Obama's national security adviser has said that anti-Semitic leaflets reportedly distributed in Ukraine were "utterly sickening" and that Obama had bluntly expressed his disgust.
Susan Rice was referring to leaflets demanding that Jews in eastern Ukraine register with a self-proclaimed local authority or face consequences. She says the leaflets had no place in the 21st century.
Rice said US Secretary of State John Kerry had forcefully conveyed that view to his Russian counterpart.
Tensions continue to simmer in eastern Ukraine, where pro-Russian protesters are demanding a referendum on autonomy and closer ties with Russia.
The Associated Press reported that pro-Russia protesters exchanged fire with the police in the town of Kramatorsk. The local TV station has also been occupied by protesters.
The local government building is where protesters are gathering together. But they said their protest will not affect the normal functioning of the government.
Russia's government has accused the US of trying to "whitewash" the use of force by the Ukrainian government against Russian speakers in the east of the country.
A statement from the Russian foreign ministry also called new sanctions from Washington aimed at the Putin government "completely unacceptable".