The US Secretary of State has warned of further sanctions on Russia if it does not de-escalate tensions in Ukraine.
In a phone call with Russian Foreign Minister Sergei Lavrov, John Kerry expressed "deep concern over the lack of positive Russian steps".
Russia blames Kiev's leaders for the collapse of last week's Geneva accord.
Ukraine's acting president earlier ordered the relaunch of military operations against pro-Russian militants in the east of the country.
It came as President Oleksandr Turchynov said two men - including local politician Vladimir Rybak - had been found dead after being "brutally tortured".
"The terrorists who effectively took the whole Donetsk region hostage have now gone too far," he said.
The US and the West accuse Russia of using undercover military to back separatists in eastern Ukraine, where public buildings are occupied in at least nine cities and towns. Russia denies involvement.
'ABSENCE OF PROGRESS'
In his conversation with Lavrov on Tuesday, Kerry "urged Russia to tone down escalatory rhetoric, engage diplomatically in the east... and issue public statements calling for those occupying buildings to disarm," according to a senior State Department official.
"Secretary Kerry also reiterated that the absence of measurable progress on implementing the Geneva agreement will result in increased sanctions on Russia," the official said.
The warning came after US Vice-President Joe Biden met Ukraine's new leaders in Kiev, and called on Russia to "stop talking and start acting" to defuse the Ukraine crisis.
The US is to provide an additional $50m (£30m) for political and economic reforms in Ukraine, including $11m to help run the presidential election due on 25 May.
AT THE FUNERALS
In the Church of the Holy Spirit in the centre of Sloviansk, an Orthodox priest chanted prayers for the dead. The bodies of three pro-Russian activists, shot dead at a makeshift checkpoint on Easter Sunday, lay in open coffins.
When the coffins were carried out of the church, the crowd outside shouted "Glory to the Heroes of the Donbass!" over and over again - Donbass being the name for the Don River basin. Church bells rang out.
The people I've been speaking to here are convinced that it was Ukrainian ultra-nationalists who carried out Sunday's attack. One woman told me she was proud to be Ukrainian, but that instability and violence was pushing people here to want closer ties to Russia.
In another US move, Washington is sending 600 troops to take part in Nato exercises in the three Baltic states and Poland.
A defence department spokesman said the decision was designed to show a strong commitment to the alliance as events unfolded in Ukraine.
Meanwhile the funerals have taken place of three men shot on Sunday during a raid on a checkpoint manned by pro-Russian separatists near Sloviansk.
The local separatists said the attack was carried out by ultra-nationalist Right Sector militants but Kiev called it a "provocation" staged by Russian special forces.
The bodies of those killed lay in open coffins at the funeral ceremony at the Church of the Holy Spirit in the centre of Sloviansk.
Announcing the decision to reactivate the military operation in eastern Ukraine, Turchynov said in a statement: "I call on the security bodies to resume and carry out successful anti-terrorist measures aimed at defending Ukrainian citizens living in the east of Ukraine against terrorists."
Kiev's military operation to end the occupation of buildings began on 16 April but was suspended over the Easter period.
Rybak, whose body was found near Sloviansk on Tuesday, was described as a local councillor for the Fatherland party in the nearby town of Horlivka. The other man killed has not yet been publicly identified.
Rybak had gone missing recently and, according to police, his body was found in a river.
"These crimes are being committed with the full support and connivance of the Russian Federation," Turchynov said.
A man by a pro-Russian barricade in the eastern Ukrainian city of Lugansk, 22 April 2014
In another incident, a Ukrainian military surveillance plane was hit by small arms fire over eastern Ukraine on Tuesday, the defence ministry said.
The aircraft, an Antonov AN-30, suffered minor damage over Sloviansk when it was targeted by automatic gunfire, according to the ministry. No-one was hurt and the plane returned safely to Kiev.
The US has previous said is planning further sanctions should Russia fail to fulfil its Geneva commitments.
The 17 April Geneva accord stipulated an immediate end to violence in eastern Ukraine and called on illegal armed groups to surrender their weapons and leave official buildings.
But Russian Prime Minister Dmitry Medvedev told the Russian parliament on Tuesday that Russia would be able to "minimise the consequences" of any further sanctions.
Ukraine has been in turmoil since last November, when Kiev was gripped by protests over whether the country should lean more towards Russia or Europe.