Three pro-Russian militants and one attacker were killed in a deadly firefight at a road block close to the separatist-held town of Slavyansk, local leader Vyatcheslav Ponomarev said.
The identity of the assailants was not known. Kiev's interim government had pledged a halt to military operations to oust the rebels until the end of the Orthodox Easter holidays on Monday.
Three pro-Russian militants and one attacker were killed in a gunbattle near the volatile eastern town of Slavyansk, Ukraine. (AFP Photo)
A pro-Russian militant at the scene told AFP that roughly twenty attackers in four cars had opened fire with automatic weapons on the rebel post early Sunday. He could not, however, confirm any casualties.
The reported violence came as the United States was pressing Russia to persuade the pro-Kremlin rebels to abide by an international accord calling for them to surrender their weapons and leave occupied public buildings.
Overnight, Orthodox leaders in Kiev and Moscow traded barbs over the Ukraine crisis as politics overshadowed traditional Easter observances.
Patriarch Filaret thundered to the faithful in pro-West Kiev that Russia was an "enemy" whose "attack" on Ukraine was doomed to failure because it was evil and contrary to God's will.
In Moscow, the patriarch of the Russian Church, Kirill, delivered a prayer for Ukraine in which he called on God in turn to put "an end to the designs of those who want to destroy Holy Russia".
Kirill said that while Ukraine was "politically" separate, "spiritually and historically" it was at one with Russia, and he prayed that it would benefit from authorities that are "legitimately elected".
In comments to be broadcast on US television Sunday, Ukrainian Prime Minister Arseniy Yatsenyuk lashed out at Russian President Vladimir Putin -- whom Kiev and Washington accuse of masterminding the insurgency in Ukraine -- for having a "dream to restore the Soviet Union".
Yatsenyuk, speaking to NBC's "Meet the Press", also condemned those who reportedly handed out pamphlets demanding Jews register or be expelled in the east of Ukraine as "these bastards" who should be brought to justice.
The United States on Saturday was reported to be flexing its military muscle in a warning to Russia, which has tens of thousands of troops massed on Ukraine's border.
The Washington Post said that the US was about to deploy ground troops to Poland and maybe Baltic states to expand NATO's presence in eastern Europe.
Poland's defence minister, Tomasz Siemoniak, was quoted saying that Poland, a NATO member, would be taking a lead role in the operation.
Washington has warned Moscow that Ukraine is in a "pivotal period" as the pro-Russian rebels refuse to comply with the Geneva accord reached Thursday by Russia, the US, Ukraine and the EU to disarm.
US Secretary of State John Kerry told Russian Foreign Minister Sergei Lavrov that "full and immediate compliance" was needed within "the next few days".
The Kremlin has snapped back by stressing its troops' deployment on Ukraine's doorstep -- an apparent warning that the situation could rapidly deteriorate if Washington follows through with a threat to impose further sanctions.
Putin has switched stances on the crisis between threatening -- saying he "hoped" he would not have to invade Ukraine -- to conciliatory, saying "no obstacle" existed to better relations with the West.
But thus far there have been no concrete moves de-escalating the worst East-West confrontation since the Cold War.
The separatist leaders in the self-declared eastern Donetsk Republic say they will not vacate public sites until the "illegal" government exits state buildings in Kiev.
If no change happens soon, a spike in tensions could occur when US Vice President Joe Biden makes a scheduled visit to Kiev on Tuesday.
He will be meeting leaders who have taken charge since the February ouster of pro-Kremlin president Viktor Yanukovych, after months of street protests that turned increasingly deadly.
Russia refuses to see the new Kiev government as legitimate, and the turmoil in Ukraine's southeast could prove an obstacle to a planned May 25 presidential election.
In concessions to the Russian-speaking militants, Ukraine's interim president and prime minister have vowed to protect the Russian language, decentralise power and hold off further military action against the separatists until at least Tuesday.
Ukraine's military has so far proven woefully inept in its efforts to dislodge the separatists. On Friday, the army said it recovered two of six armoured vehicles captured by rebels during a disastrous military operation earlier in the week.
A poll published Saturday suggested the majority of inhabitants in Ukraine's restive east, while suspicious of Kiev's authorities, had no desire to be subsumed into the Russian Federation.
The Russian-language Weekly Mirror newspaper said 52.2% of those surveyed for a poll in the separatist hub of Donetsk by Kiev's Institute for International Sociology were against coming under Russian rule while 27.5% were in favour.