A Moscow court extended the detention of Ukrainian pilot Nadiya Savchenko on Tuesday
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.
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.
Russia denies Western and Ukrainian accusations of sending troops and arms to support the rebels and has warned the West that sending arms to Ukraine would worsen the crisis.
US President Barack Obama said on Monday that he had not ruled out supplying "lethal defensive weapons" to Ukraine if diplomacy failed.
Residents in Kramatorsk gathered to examine a rocket stuck in the ground after Tuesday's shelling
Earlier, Ukrainian President Petro 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.
Kramatorsk was the scene of fierce fighting in 2014 but it some way from the current conflict zone
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.
Meanwhile, Andriy Biletsky, commander of the Azov battalion - an ultra-nationalist volunteer force based in Mariupol affiliated with Ukraine's interior ministry - confirmed to the BBC that its fighters were advancing and fighting pro-Russian rebels outside the southern port city.
"We have taken the villages of Shyrokine, Pavlovo, Kominternovo. We are currently moving towards Novoazovsk."
On Saturday, Ukraine said rebels appeared to be massing forces for attacks on strategic towns, including Mariupol.
The port city lies in a key coastal position 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.
Mariupol is in a highly strategic position, sitting between rebel-held eastern areas and CrimeaA Moscow court extended the detention of Ukrainian pilot Nadiya Savchenko on Tuesday
The Kremlin warned the West ahead of Wednesday's proposed peace talks against sending weapons to the Ukrainian government or putting pressure on Russia.
Russian President Vladimir Putin's spokesman, Dmitry Peskov, said that any talk about imposing new sanctions on Russia or arming the Ukraine government would destabilise the situation in Ukraine.
'Strong will'
Germany's foreign ministry said senior officials from Germany, France, Russia and Ukraine were holding talks in Minsk on Tuesday to iron out differences before its leaders met to seek an agreement.
The proposed summit on Wednesday is expected to focus on the creation of a demilitarised zone of 50-70km (30-45 miles) around the current front line, as well as the withdrawal of heavy weapons.
French President Francois Hollande said he was going to Minsk with the "strong will" to get a deal.
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 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.