At least two people were killed in a gunfight early on Sunday near a Ukrainian city controlled by pro-Russian separatists, testing an already fragile international accord that is supposed to defuse Ukraine's armed stand-off.

Hours earlier, Ukraine's Western-backed government in Kiev had declared a truce to coincide with the Easter religious holiday, giving international mediators an opportunity to try to persuade armed pro-Russian groups to disarm.

The crisis over Ukraine has dragged relations between Moscow and the West to their lowest ebb since the Cold War, and risks escalating this week with a U.S. threat of further sanctions against Moscow if the pro-Russian separatists do not pull back.

A deal signed in Geneva last week by the European Union, Russia, Ukraine and the United States agreed that illegal armed groups would go home, but so far they have shown no signs of budging, leaving the accord looking threadbare.

Separatist militiamen near the eastern Ukrainian city of Slaviansk told Reuters that a convoy of four vehicles had approached their checkpoint at around 2:00 a.m. (4 P.M. EDT) and opened fire.

"We had three dead, four wounded," one of the separatist fighters, called Vladimir, told Reuters at the checkpoint, where there were two burned-out jeeps.

He said the separatists returned fire and killed two of the attackers, who he said were members of Right Sector, a group loosely aligned with the government in Kiev. Slaviansk has been controlled by separatists since last weekend.

A Reuters cameraman at the scene said he saw the bodies of two local fighters, one with what appeared to be gunshot wounds to the head and face. One of the dead was dressed in camouflage fatigues, the other in civilian clothes.

In Kiev, the Interior Ministry said one person had been killed and three injured in an armed clash. It said police were trying to establish more details of what happened.

The deaths were the first in armed clashes in eastern Ukraine since the Geneva accord was signed on Thursday.

A senior mediator with the Organization for Security and Cooperation in Europe set off for eastern Ukraine on Saturday to try to persuade pro-Russian groups to lay down their arms, in line with the Geneva accord.

But the attack near Slaviansk is likely to harden their position that they will not lay down their arms because they believe they are under threat of violent attack from forces loyal to Kiev.

The United States government has said that it will impose further sanctions on Moscow if, by early this week, there is no measurable sign that the pro-Russian separatists are complying with the accord.

No will to move

The crisis in Ukraine began late last year when President Viktor Yanukovich turned his back on closer ties with Europe, prompting protests in the capital. They led to him fleeing Kiev, and a pro-Western interim administration taking over.

Soon after, Moscow used its military to back separatists in Ukraine's Crimea Peninsula, before Russian President Vladimir Putin signed a document annexing Crimea. The United States and European Union responded by slapping sanctions on Russian officials.

The crisis has now shifted to the east of Ukraine, where armed groups of pro-Russian separatists have seized public buildings, saying they reject Kiev's rule. Adding to the tension, Russia has shifted extra troops to the border with Ukraine.

Russia argues that it acted only to protect ethnic Russians in Ukraine from an administration in Kiev which they say was installed in an illegal coup d'etat, which they allege has links to the far-right and discriminates against Russian speakers.

After a meeting on Saturday in the Ukrainian capital with diplomats from the four parties to the Geneva accord, Swiss envoy Christian Schoenenberger, whose country is chair of the OSCE, said its monitors had spoken to several activists occupying public buildings.

"For the time being the political will is not there to move out," he said.

"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," he told reporters.

Goodwill gesture

The Ukrainian foreign ministry had promised that, as a gesture of goodwill for the Easter holiday, it would suspend the active phase of an operation it had launched to re-assert its authority in the east of the country.

In another sign of reconciliation, the Interior Ministry issued an Easter message which asked members of the ministry's disbanded Berkut unit to help defend Ukraine's unity.

In the days when Yanukovich was clinging to power in Kiev, Berkut members are alleged to have been responsible for shooting dead dozens of protesters. Their unit was disbanded, and some of them have joined the pro-Russian separatists.

However, many people in eastern Ukraine, which has a large Russian-speaking population, feel deep suspicion of the new authorities in Kiev.

The separatists say they will not leave the buildings they have occupied until the pro-Kiev protest groups occupying Independence Square - scene of the months-long protests against Yanukovich, also go home.

They want guarantees that they will be given a large degree of autonomy from Kiev and that protections of their rights will be enshrined in a new constitution.

At Easter church services in Kiev and in Moscow, senior clergymen issued sharply contrasting appeals for peace.

"In these Easter days our prayers to God are for the people of Ukraine, for a reconciliation of enmity, for an end of violence, for people's love for each other, so that they should not be divided," Patriarch Krill, head of the Russian Orthodox Church, said in a recorded video message.

In his Easter message, Patriarch Filaret, head of Ukraine's Orthodox Church, condemned what he described as Russia's aggression against his country.

"God cannot be on the side of evil, so the enemy of the Ukrainian people is condemned to defeat," he said. "Lord, help us resurrect Ukraine."