Last Updated Apr 20, 2014 6:05 PM EDT
DONETSK, Ukraine - Within hours of an Easter morning shootout at a checkpoint manned by pro-Russia insurgents in eastern Ukraine, Russia's Foreign Ministry issued a statement blaming militant Ukrainian nationalists and Russian state television stations aired pictures of supposed proof of their involvement in the attack that left at least three people dead.
A pro-Russian gunman told CBS News: "They started shooting at us, and threw stun grenades. A sniper was firing at people who tried to run to the village."
The Ukrainian Security Service, however, said the attack was staged by provocateurs from outside the country, and some even tried to blame Russian special forces. And the presented evidence - particularly a pristine business card said to have been left behind by the attackers - was met with widespread ridicule in Ukraine, where it soon had its own Twitter hashtag.
The armed clash near the city of Slovyansk appears to be the first since an international agreement was reached last week in Geneva to ease tensions in eastern Ukraine, where pro-Russian supporters have seized government buildings in at least 10 cities.
In Moscow, the Russian Foreign Ministry blamed the clash on the Right Sector, a nationalist Ukrainian group that has supported the interim government in Kiev, the capital.
The Right Sector denied any role, saying Russian special forces were behind the clash, Reuters reported.
The self-proclaimed mayor of Slovyansk appealed to Russian President Vladimir Putin on Sunday to send in peacekeeping troops to protect Russian speakers from Ukrainian nationalists.
"They want to make us slaves. They don't talk to us, but simply kill us," Vyacheslav Ponomaryov said during a news conference in Slovyansk shown on Rossiya state television.
Yuri Zhadobin, who coordinates the pro-Russia unit manning the checkpoint in the village of Bylbasivka, told The Associated Press he was with about 20 men celebrating Easter when unknown men drove up in four vehicles and opened fire about 3 a.m.
"We began to shoot back from behind the barricades and we threw Molotov cocktails at them," Zhadobin said. Two of the vehicles caught fire and the attackers fled in the other two, he said.
The Ukrainian Interior Ministry's office in the eastern Donetsk region said three people died in the attack and three others were wounded. The statement said some of the attackers were also killed or wounded, but the number wasn't known. Russian state television reported that two of the attackers were killed.After the deaths, Russia questioned whether Ukraine's Western-backed government was complying with the Geneva agreement.
The fault for the failure of the Geneva agreement could determine whether or not the United States and its European partners impose tougher sanctions on Russia.
Two members of the Senate Foreign Relations Committee called Sunday for tougher Western sanctions against Russia to include its petrochemical and banking industries and warned that Moscow thus far has ignored U.S. and European efforts to persuade it to back off its confrontation with Ukraine.
"We've helped in many ways to create the problems that exist there. And to leave them alone in the manner that we're leaving them alone to me is just unconscionable," Sen. Bob Corker, the committee's senior Republican member, said on NBC television's "Meet the Press."
"I don't think Putin really believes we're going to punish them in that way," he said.
Democratic Sen. Chris Murphy of Connecticut, a member of the same committee, said: "I think the time is now to rapidly ratchet up our sanctions, whether it's on Russian petrochemical companies or on Russian banks."
"If Russia does get away with this, I do think that there's a potential that a NATO ally is next. And, yes, there will be economic pain to Europe (under tightened sanctions). But it's time for them to lead as well," Murphy said.
President Barack Obama has said his administration is prepared to take further action against Russia if diplomatic efforts to destabilize the conflict fail.
Vice President Joe Biden plans to be in Kiev, the Ukrainian capital, on Monday and Tuesday to meet with government leaders and democracy advocates.
The truce agreement signed in Geneva last week by the European Union, Russia, Ukraine and the United States agreed that illegal armed groups would go home.
So far, the pro-Russian militants have shown no signs of budging, though there was some hope of progress after Kiev said it would not move against the separatists over Easter, and international mediators headed to eastern Ukraine to try to persuade them to disarm.
CBS News met with pro-Russian separatists who have no intentions of leaving the public buildings they've taken over.
They've occupied a building in Donetsk for nearly two weeks, and have barricaded themselves inside with razor wire. The insurgents are demanding a separate state, or at least more autonomy for their region.
They are suspicious of Ukraine's pro-Western government in Kiev, and want closer ties with Moscow.
They have now begun calling themselves the Republic of Donetsk. In the republic's offices CBS News met spokeswoman Yekatarina Mihaylova.
Mihaylova told CBS that they will only leave if there's a referendum on the future of eastern Ukraine, and if rival protesters in the capital Kiev also go home.