An international agreement to defuse the crisis in Ukraine was all but shredded on Sunday after a shootout in the separatist town of Slavyansk.

Three days after the Geneva deal brought modest hopes for a resolution to the gravest east-west stand-off since the end of the cold war, the midnight incident at a checkpoint – in which reports said as many as five people were killed – unleashed a torrent of accusations and counter-accusations that bodes ill for international peacemakers.

Russia claimed that far-right Ukrainian nationalists opened fire at the checkpoint just outside the town, seized by an armed pro-Russian militia two weeks ago. The foreign ministry in Moscow accused Kiev of failing to disarm "extremists and terrorists" and blamed the clash on the Right Sector, a nationalist Ukrainian group that has supported the pro-Western interim government in Ukraine.

The new self-proclaimed mayor of Slavyansk, Vyacheslav Ponomaryov, said Russian troops were urgently needed to protect the civilian population. He threatened to "personally shoot" Ukraine's interior minister Arsen Avakov if he could.

The authorities in Kiev described the incident in the early hours of Sunday as a "crude provocation", made for Russian TV. They said some of the details of the shootout were so implausible as to be ridiculous.

Ukraine's intelligence service said its Russian military counterpart, the GRU, had staged it with help from criminals.But Russian channels claimed that a business card belonging to Dmitry Yarosh, the leader of the far-right Right Sector, had been left by the "attackers".

Also discovered were crisp new $100 bills, a satellite map of the area, and a second world war German gun, they reported.

The death toll and the allegiance of those involved were hard to confirm independently. Armed militias manning checkpoints and flying the Russian flag outside Slavyansk were reluctant to allow the Guardian to investigate on Sunday. At the bridge into the town, one commander armed with a pistol told the Guardian to leave. He punched the car with his fist, leaving a dent. "Get out of here," he screamed.

The Euromaidan PR tweet about the return of the Ukrainian flag in Yenyakiyevo.

Ukraine's new leaders, and many in the west, fear such an incident could be used as a possible pretext for the kind of Russian military manoeuvre that rapidly led to the annexation of Crimea last month. Under the Geneva agreement between Russia, Ukraine, the US and EU, illegal groups are meant to end occupations of official buildings and give up weapons. But pro-Russian militias which grabbed administrations in at least 10 eastern towns two weeks ago have mostly refused to budge.

In one town, Yenyakiyevo, activists did go home on Sunday. The Ukrainian flag is back on the roof in a rare piece of good news for Kiev's pro-western government, which appears powerless in the face of fast-moving events.

Ukraine's new prime minister, Arseniy Yatsenyuk, who is hosting the US vice-president, Joe Biden, this week, told US television that he wanted greater support from America in the face of Russian aggression. "We need a strong and solid state," he told NBC. "We need financial and economic support. We need to overhaul the Ukrainian military. We need to modernise our security and military forces. We need real support."

But the US ambassador to Kiev warned later that the US could do little to tilt the military balance in Ukraine's favour. "The geography and balance of power is such, there is no military solution to this crisis," Geoffrey Pyatt told CNN. "The fact is that militarily, as Crimea showed, Ukraine is outgunned."

Ukraine's interior ministry said none of its forces had carried out an operation around Slavyansk over the weekend. It described the town 90km north of the regional capital Donetsk, as "the most dangerous place in Ukraine, in view of the presence in the town of foreign saboteurs and illegal armed groups."

It added: "At the same time one cannot but suspect the speed with which camera crews from Russian TV stations appeared at the scene of the shooting, and the obviously staged subject matter of news reports in the Russian media."

It noted that the Russian journalist Dmitry Kiselyov had broken the story. Kiselyov is close to Vladimir Putin and notorious for his radical nationalist views. The US and EU last month imposed a visa ban on him as part of the sanctions package designed to punish Russia for annexing Crimea.

But the Russian foreign ministry insisted that Ukrainian ultra-nationalists were behind the incident, which took place between Slavyansk and the town of Bylbasovka. "The Russian side is outraged by the provocation, which indicates that Kiev is unwilling to put in check and disarm nationalists and extremists," it said. Moscow, it added, "insists on the strict implementation of the Ukrainian side of its commitments to de-escalate the situation in eastern Ukraine."

The Right Sector denied any involvement. Its spokesman, Artem Skoropadsky, told Reuters: "It is a blasphemous provocation from Russia: blasphemous because it took place on a holy night for Christians, on Easter night. This was clearly carried out by Russian special forces."

Ukrainian bloggers, meanwhile, poked fun at the Russian media claim that a business card belonging to the Right Sector's leader had been discovered. They tweeted photos of the same card on the moon, next to a lunar module, and on the wall of the Sistine chapel. Many pointed out that the card had implausibly survived a fire that entirely gutted two bullet-ridden cars.

The Geneva deal was designed to pave the way for an Easter truce, at the very least. And religious observation was possible in much of the east on Sunday. Locals in Slavyansk were handing out traditional sugar-topped Easter cakes. Offering a slab, Leonid Bikadanov, 43, said he was a member of the people's militia. "I'm no-one important," he said. "I've got this to protect me," he added, lifting a camouflage jacket to reveal verses from the Bible written on his belt.

But the situation on the ground in and around Slavyansk appeared to be darkening. One Ukrainian expert suggested that more irregular gunmen and criminal elements had poured into the area in the past 48 hours. There are unconfirmed reports of Roma families being forced to leave. Youths in black balaclavas, with several carrying pistols, ran checkpoints and stopped all cars. A few days ago, they were unarmed.

About 10 miles north of the town, locals were visiting Svyatogorsk monastery, built around a a steep hill and a series of caves, and overlooking the picturesque Seversky Donets river. In previous years tens of thousands of people flocked to the site. On Sunday, however, there was only a trickle of families, carrying brown wicker baskets filled with Easter eggs and cake.

"People are scared. They don't want to come out," Viktor Oneskehnko, a 53-year-old doctor and Chernobyl survivor said, walking with his wife and daughter towards the monastery's white and turquoise 19th-century church. Oneshenko said he supported Ukraine's territorial integrity. He was contemptuous of the separatists who he said had hijacked Slavyansk. "They're opportunists and mafia", he said.

"The separatists are actually not that numerous. Most people around here support Ukraine," he added. "Russian TV has zombified some. And young guys often support maximalist positions." Oneshenko said he was against the "Donetsk People's Republic", a self-elected pro-Moscow group which is demanding a referendum on the region's status before 11 May.

"We don't want it. It means marauding. It means stopping people in the street. It means being afraid. We want peace," he said. He conceded that some older people were keen on the idea of union with Russia because they thought they would get bigger pensions. "I've travelled all over Russia. I've seen how people live there. They [pro-Russian pensioners in the east] are deluding themselves."

Additional reporting by Dan Roberts in Washington