Fighting has surged in eastern Ukraine as government forces and pro-Russian rebels try to make gains ahead of expected peace talks on Wednesday.
Rebels carried out rocket attacks on a key military base and a residential area in Kramatorsk, officials say, killing at least seven civilians.
Meanwhile, Ukraine's volunteer Azov battalion has launched an offensive against separatists around Mariupol.
More than 5,400 people have died since the conflict began last April.
Ukraine and the West accuse Russia of sending troops and arms to support the rebels, but Russia denies this.
The leaders of Ukraine, Russia, France and Germany are due to meet in the Belarusian capital Minsk on Wednesday to hammer out a peace deal after months of fighting.
The summit is expected to focus on the creation of a demilitarised zone and the withdrawal of heavy weapons.
French President Francois Hollande said he was going to Minsk with the "strong will" to get a deal.
The White House says US President Barack Obama spoke with Ukrainian President Petro Poroshenko on Tuesday ahead of the proposed talks.
Mr Obama has refused to rule out supplying "lethal defensive weapons" to Ukraine if diplomacy fails, but Russia has warned that such a move would worsen the crisis.
Earlier, President Poroshenko told parliament that the government's military headquarters at Kramatorsk airfield had been shelled by rebels.
At least seven people were killed and 16 wounded when a residential area was also hit, the government-controlled Donetsk regional administration said. Ten people were injured at the military base, it added.
Kramatorsk, some distance west of the current conflict zone, was the scene of major fighting until July, when pro-Russian separatists retreated.
Local authorities said the rockets were fired from the rebel-controlled Horlivka area, which is about 50km (30 miles) away from the city. The separatists denied firing the rockets.
Julia Dzuba, a resident of Kramatorsk who caught the shelling on film as it neared the apartment she lives in with her young child, told the BBC: "I was online, reading news, and then I heard boom, boom!"
"This is much worse than last summer," she said. "[T]hey are shooting at each other, and we are the ones who suffer."
Rival agendas at Ukraine talks
Ukraine: Restore government authority over breakaway areas, though Donetsk and Luhansk regions could get greater self-rule; disarm rebel forces; withdrawal of Russian troops; restore Kiev's control over Ukraine-Russia border; full prisoner exchange.
Pro-Russian rebels: Separation from rest of Ukraine and recognition of "people's republics" of Donetsk and Luhansk; no disarmament of separatist forces; amnesty for separatist leaders.
Russia: Legal guarantees for rights of Russian-speakers in eastern Ukraine; full autonomy for Donetsk and Luhansk in a federal system - not necessarily independence; no return of Crimea to Ukraine; withdrawal of Ukrainian troops from combat zone.
EU and US: Restore Ukraine's territorial integrity; end Russian intervention in eastern Ukraine - withdrawal of all Russian troops and heavy weapons; effective monitoring of Russia-Ukraine border and demilitarised zone between the combatants; full democracy in Donetsk and Luhansk.
The surge in fighting comes a day after separatists said they had cut off a key supply road to Debaltseve, a railway hub near the rebel-held city of Donetsk. The military says the battle is ongoing.
The BBC's James Reynolds in Donetsk says the intense clashes are a sign that both sides want to go into the Minsk talks holding as much territory as they can.
Earlier, the commander of an ultra-nationalist volunteer group loyal to Kiev said its forces, which are based in Mariupol, were advancing on pro-Russian rebels outside the southern port city.
"We have taken the villages of Shyrokine, Pavlovo, Kominternovo. We are currently moving towards Novoazovsk," Andriy Biletsky, commander of the Azov battalion, told the BBC.
The advance comes just days after Ukraine said rebels were massing forces for attacks on strategic towns, including Mariupol, which lies between rebel-controlled areas and the Crimean peninsula.
Russia's Ria news agency reported on Tuesday that more than 600 Russian troops had started exercises in Crimea, which was annexed by Russia last year.
In another development, a court in Moscow extended the detention on Tuesday of Nadiya Savchenko, a Ukrainian military pilot who is accused of killing of two Russian journalists in eastern Ukraine last year.
Ms Savchenko, who is seen as a national hero in Ukraine, has been on hunger strike since December to protest against what her lawyers call absurd and politically-motivated charges.
She ended up in Moscow after being captured by rebels near Luhansk. Ukraine has accused Russia of abducting her and has demanded she be released and allowed to go home.
Ukraine's war: The human cost
- 5,486 people people killed and 12,972 wounded in eastern Ukraine
- Fatalities include 298 people on Malaysia Airlines flight MH17 shot down on 17 July
- 263 civilians killed in populated areas between 31 January and 5 February
- 5.2 million people estimated to be living in conflict areas
- 978,482 internally displaced people within Ukraine, including 119,832 children
- 600,000 fled to neighbouring countries, of whom more than 400,000 have gone to Russia
Source: Figures from UN report, 6 February