Ukrainian forces and anti-government fighters clashed just east of the strategic port of Mariupol on Friday, hours before envoys from Ukraine and Russia were expected to announce a ceasefire as the starting point for a wider peace plan.
Renewed gunfire and artillery fire were also heard in Donetsk, the rebels' main stronghold in eastern Ukraine, from near the city's airport which remains in government hands.
Ukraine says its forces are trying to repel a big offensive by the rebels to take Mariupol, a port city of around 500,000 on the Sea of Azov crucial for its steel exports. It stands about halfway between Russia and the Russian-annexed Crimea region.
"Our artillery has come and is being deployed against the (pro-Russian) rebels," the mayor of Mariupol, Yuri Khotlubey, told Ukraine's 112 TV channel.
The Azov volunteer militia said in a social media post that its men, along with Ukrainian troops, had staged a counter-offensive in the direction of Novoazovsk, a coastal town further east near the Russian border that was seized by rebels in late August. This report could not be immediately confirmed.
"We are fighting for every meter of our land. The situation is extremely difficult," it said in the post.
Mariupol became a major focus of concern for Ukraine after the rebels broke away from their main strongholds further north in late August - backed, Kiev says, by Russian regular forces.
Russia denies sending troops and weapons into Ukraine, despite what NATO says is overwhelming evidence to the contrary.
A Ukrainian army doctor showed the fragment of a shell he said had killed a woman and two children in a village near Mariupol. "It was a Russian rocket, we know it from its markings," he said.
Representatives from Ukraine, the pro-Russian rebel leadership, Russia and Europe's OSCE security watchdog are expected to meet in the Belarussian capital Minsk and to sign around 0700 ET a peace plan for the region that will impose a ceasefire by both sides.
However, few in eastern Ukraine, wearied by nearly six months of conflict, have much hope that a ceasefire can hold and some said it was a bad idea that would only benefit the enemy.
"A ceasefire would be a disaster, we would lose everything. By fighting we can resist the invasion and send them back. With a ceasefire they will consolidate and carry on after a while," said Ukrainian soldier Taras.
Another Ukrainian soldier who gave his name as Mykola said Ukrainian President Petro Poroshenko - who was attending the second day of a NATO summit in Wales on Friday - would "betray the country" if he backed a peace plan at this time.
"If he goes for a peace plan, then all these dead and wounded and exiled and all the homes burned and jobs lost and money lost, it was all for nothing," he said.
In rebel-held Donetsk, where residents mostly tend to blame the Ukrainian side for the conflict, scepticism was also strong.
"I doubt Ukraine would go for any ceasefire. Poroshenko may announce it for the army but there are also the Kolomoisky battalions," said Denis Tikhinov, 22, who worked for a computer servicing firm before it shut because of the fighting.
He was referring to battalions formed by Ihor Kolomoiksy, a wealthy businessman and governor of the Dnipropetrovsk region, to help fight the pro-Russian separatists.
"When the first ceasefire was announced by Poroshenko, Kolomoisky said there would be no such thing and gave orders to his battalions to go on destroying the city and civilians."
On Friday morning, people queued to get water from cisterns, to sign up for humanitarian aid and to withdraw money from the cash machine of one of the few banks still working in the city, which had a pre-war population of about one million.
"I have no hopes. Poroshenko is a traitor, he makes promises but he's just lying to the people," said pensioner Lidia.