(CNN) -- Mystery surrounds a shooting incident on a country road in eastern Ukraine that left several people dead and ratcheted up tensions in the region, where pro-Russian groups have seized government buildings and set up roadblocks in defiance of authorities in the Ukrainian capital, Kiev.
In the early hours of Sunday morning, according to pro-Russian groups in the town of Slaviansk, one of their roadblocks to the west of the town came under attack. They say three or four vehicles approached the roadblock, and their occupants opened fire on the barricades' defenders.
The new pro-Russian administration in Slaviansk said six people were killed in the shoot-out.
CNN was not able to confirm the number of dead. Efforts to contact the hospital in Slaviansk were unsuccessful. But pro-Russian leaders in Slaviansk displayed a body briefly outside the State Security building in the town, which they have occupied for a week.
They said the body was one of the alleged assailants.
There were conflicting reports on the number of casualties.
A statement on the Interior Ministry's website said that four cars with unknown occupants approached a checkpoint at the entrance to the city and opened fire on people manning it, and shots were returned.
Three people were killed and three were wounded, that statement said. Two of the wounded received medical care but refused to be sent to the hospital.
There were about a dozen people in two cars that drove away from the scene in the direction of the Kharkiv region, according to the statement, and the two remaining cars at the scene were set on fire and destroyed.
Pro-Russian protesters at the roadblock told CNN on Sunday that as the attack got under way, they called for support, and armed men arrived to engage the attackers. Two burned-out cars were still at the scene Sunday afternoon, one of them riddled with bullet holes on one side.
Along with the body outside the State Security building, pro-Russian leaders displayed what they claimed were an identity tag and card as evidence that the attack was carried out by the ultranationalist Ukrainian "Right Sector," along with substantial amounts of U.S. cash and ammunition.
The Right Sector immediately denied any of its members were in the area. "The information that one of our members was shot in Slaviansk is false," said Borislav Bereza, head of the information department for Right Sector.
"We don't have ID cards with numbers. We only have ID cards with letters, where we mention the department where the person works," said Bereza.
CNN called the number on the calling card and reached a woman who seemed to be surprised she had been called. She said that she was in Kiev and had no relation to anyone in Right Sector.
In the hours after the attack, the self-declared mayor of Slaviansk, Vyacheslav Ponomarev, called for a Russian "peacekeeping force" to protect against the National Guard and the Right Sector.
The Ukrainian State Security Service, the SBU, said in a statement that "armed offenders and saboteurs who are terrorizing the local population in Slaviansk had "resorted to cynical provocation." It said one person had died in the incident.
Another deadly shooting
The shooting is the second deadly incident in the last four days in eastern Ukraine. On Wednesday night, three people were killed during a demonstration outside a Ukrainian military base in the southern city of Mariupol. They appear to have been shot dead by Ukrainian soldiers after attempting to break into the base and throwing Molotov cocktails over its walls.
The two sides in the crisis invariably give very different accounts of incidents of violence. Pro-Russian groups see the hand of "fascists" from Kiev in many of the incidents, while Ukrainian officials insist that Russian Special Forces have been sent to Ukraine to stir up trouble.
As the occupation of buildings continued in about a dozen towns and cities across eastern Ukraine, Interior Minister Arsen Avakov announced on his Facebook page that he was traveling to eastern Ukraine to inspect the readiness of troops.
International monitors from the Organization for Security and Co-operation in Europe continue to visit many of the affected towns, but have had no success so far in persuading groups that have taken over buildings to relinquish them. The OSCE presence was mandated by an agreement among Russia, the United States and the European Union last week to try to negotiate the handover of the buildings. In three towns, pro-Russian protesters and militants have made it clear to CNN they have no intention of moving until the "illegal" government in Kiev also moves out of official buildings.
Putin's 'final destination'?
On Sunday, Ukrainian Prime Minister Arseniy Yatsenyuk appeared on NBC's "Meet the Press."
"(Russian) President (Vladimir) Putin has a dream to restore the Soviet Union," he said. "And every day, he goes further and further. And God knows where is the final destination."
"The world has a reason to be concerned about Putin's intention," Yatsenyuk said. "Because what Russian Federation did, they undermined the global stability."
The United States is trying diplomatic measures to reduce tensions in Ukraine.
Vice President Joe Biden will be in Kiev this week, where he is expected to meet with various leaders, including acting President Oleksander Turchynov.
Geoffrey Pyatt, the U.S. ambassador to Ukraine, told CNN's Candy Crowley on Sunday that he's seen progress to that end. He had just met with Ukrainian Foreign Minister Andriy Deshchytsia and the ambassador who heads the OSCE's special monitoring mission, along with his European Union and Russian counterparts.
"I think we all reaffirmed today in this setting our collective commitment to trying to make the Geneva framework a success," he said on CNN's "State of the Union." "There are obviously some real challenges at this point," including the violence in Slaviansk.
"But we also believe that there has been some progress. I'm seeing reports this morning that at least one of these (occupied) government buildings now has a Ukrainian flag flying over it," he said. "And the OSCE has monitors on the ground who are reaching out, engaging with local political elites, seeing if there's a way to de-escalate the crisis."
There is "no military solution" to the crisis, Pyatt said. "It has to be solved through diplomacy."
CNN's Elena Sandyrev, Phil Black, Alla Eshchenko and Lena Kashkarova contributed to this report.