Pro-Russian separatists said on Monday that up to 20 of their fighters may have been killed in clashes with government troops in the eastern Ukrainian city of Slaviansk.
“We have many dead. Maybe more than 20 people,” a rebel representative told the Interfax news agency.
He added that the militias managed to stop government forces from advancing further into the city after “great trouble.”
The rebels said earlier that between 12 and 15 of their men had been injured.
Ukrainian Interior Minister Arsen Avakov said that government soldiers were killed during the operation, giving no figure. Avakov only confirmed that eight men were injured, the Interfax Ukraine news agency reported.
Avakov, who was speaking to reporters at a camp north of Slaviansk, said that the rebels were using heavy weapons, including mortars.
The pro-Western government in Kiev on Friday started a fresh attempt to quash the rebellion, which it says is actively supported by Russia.
Commanders say that Ukrainian army and Interior Ministry troops have fully encircled the city of more than 100 000 people.
Avakov confirmed that government forces took a television tower in the southern suburb of Andreyevka.
Acting President Oleksandr Turchynov promised in a TV interview on Sunday that the operation “will continue and bring results.” However, Turchynov admitted that the operation was hampered by popular support for the rebels.
“Let's face it - citizens of this region support the separatists, and this considerably complicates the anti-terror operation,” he said on Ukraine's Channel Five.
Past government offensives in the region were thwarted by unarmed civilians stopping armoured vehicles and soldiers' defections. Turchynov also accused Russia of waging a war against Ukraine and seeking to destabilize the country in the run-up to the May 25 early presidential elections.
Interior Minister Avakov said earlier on Monday that he sent a battalion of the newly formed national guard to Odessa and that he would later travel to the Black Sea city himself.
At least 46 people were killed and more than 200 injured in clashes between pro-Russian and pro-Ukrainian protesters in the city on Friday.
Most victims died when a trade union building burnt down after activists traded Molotov cocktails.
The European Union said on Monday that Ukrainian Prime Minister Arseniy Yatsenyuk and his government are to visit the European Commission in Brussels next week.
The visit, on May 13, is aimed at supporting Ukraine in the long- and short-term, “to undertake the political and economic reforms that are necessary for the country,” the commission said.
The talks are to include a meeting between Yatsenyuk and European Commission President Jose Manuel Barroso.
Swiss Foreign Minister Didier Burkhalter, who holds the country's rotating presidency and chairs the Organisation for Security and Co-operation in Europe (OSCE), will hold talks with Russian President Vladimir Putin on Wednesday, his ministry said.
Meanwhile, the Russian Foreign Ministry presented a report of human rights abuses in Ukraine to Putin.
The “Whitebook”, published on the Kremlin website in Russian and English, demands and end to the current “onslaught of racism, xenophobia, ethnic intolerance and glorification of the Nazis.”
It warned that otherwise there will be “devastating consequences for peace, stability, and democratic development in Europe.” - Sapa-dpa