Arsen Avakov said on his Facebook page that one Ukrainian security officer was killed, and five others wounded in a gunfight with pro-Russian activists on April 13.
Avakov said there had been an "unidentifiable number" of casualties on the side of the pro-Russian activists.
He said around 1,000 people were giving support to the separatists.
He said separatists had started using civilians as "human shields." He said security forces had begun to "regroup," but gave no other details.
Slovyansk is one of several eastern Ukrainian cities where armed pro-Russian activists on April 12 stormed police stations.
Media reports said the gunfire erupted when security forces on April 13 approached a roadblock set up by the separatists.
U.S. Ambassador to the UN Samantha Power said the latest events in Ukraine bore "the telltale signs of Moscow's involvement."
Power told ABC television on April 13: "It's professional, coordinated. Nothing grassroots about it."
She also said that the United States was prepared to step up sanctions "if actions like the kind we've seen over the last few days continue."
Meanwhile, Ukrainian media report that pro-Russia separatists have seized the mayor's office in the city of Mariupol. The reports say the building was seized by the separatists after a peaceful rally by some 1,000 pro-Russia protesters.
The reports said police did not try to stop the takeover.
In the eastern city of Kharkiv, several people were reported hurt in clashes between pro-Russia protesters and pro-Ukraine demonstrators. Reports said a group of pro-Moscow protesters attacked pro-Kyiv demonstrators after the two sides held separate rallies earlier on April 13.
WATCH: A Ukrainian military helicopter swept over Slovyansk early on April 13 as separatist gunman maintained positions behind barricades outside the city's police station. (Reuters) The Ukrainian government has accused Russia of "aggression" as attacks on government buildings and police headquarters spread in eastern Ukraine, including Slovyansk, Donetsk, Kramatorsk, and Krasny Liman.
Correspondents say the highly organized offensive by armed men, many of them masked and in unmarked uniforms, in eastern Ukrainian cities was reminiscent of that which took place in Crimea in March.
In a statement on April 13, NATO Secretary-General Anders Fogh Rasmussen said he was "extremely concerned" about the escalation of tensions in eastern Ukraine.
Rasmussen denounced a "concerted campaign of violence by pro-Russian separatists, aiming to destabilize Ukraine as a sovereign state."
Drawing parallels with Ukraine's Crimea region, which Russia annexed last month after deploying forces there, Rasmussen added, "The reappearance of men with specialized Russian weapons and identical uniforms without insignia, as previously worn by Russian troops during Russia's illegal and illegitimate seizure of Crimea, is a grave development."
Rasmussen called on Russia to "de-escalate" the situation and to pull back its troops from the area around Ukraine's border.
"Any further Russian military interference, under any pretext, will only deepen Russia's international isolation," he added.
EU foreign-policy chief Catherine Ashton urged Russia to "cease any further actions aimed at destabilizing Ukraine."
She also praised Kyiv's leaders "for pursuing their law-and-order operations in a measured way, in order to establish the authority of the state."
Britain's Foreign Office described the occupation of government buildings in eastern Ukraine as "a dangerous escalation."
"Assumptions that Russia is complicit are inevitable as long as Moscow does not publicly distance itself from these latest lawless actions," it added.
Swedish Foreign Minister Carl Bildt, who is in Ukraine, described the unrest in a Twitter post as "a coordinated armed action to seize control over key parts of Eastern Ukraine," which "would not have happened without Russia."
The U.S. ambassador to Ukraine, Geoffrey Pyatt, wrote on Twitter on April 13, "Militants in eastern Ukraine were equipped with Russian weapons and the same uniforms as those worn by Russian forces that invaded Crimea."
Russia annexed Crimea following a March 16 referendum that Ukraine and the West denounced as illegal.
Russia has warned Kyiv against using force against pro-Russia activists in eastern Ukraine. The activists are demanding a referendum on autonomy and possibly joining Russia.
Russian Foreign Minister Sergei Lavrov warned on April 12 that any armed action by Ukrainian authorities in eastern Ukraine would put planned four-party talks at risk.
The Geneva talks on April 17 are to be attended by Russia, Ukraine, the United States, and the European Union.