Pro-Russian separatists have reportedly stepped up attacks
Fighting has surged in eastern Ukraine as government forces and pro-Russian rebels try to make gains ahead of possible peace talks on Wednesday.
Separatist forces have carried out rocket attacks on a key military headquarters and a residential area at Kramatorsk, officials say.
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 hope 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 supplying 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.
This image, which the BBC is not able to verify, appears to show a shell in the ground in Kramatorsk
Ukrainian President Petro Poroshenko told parliament on Tuesday that the government's military headquarters at Kramatorsk airfield had been shelled by rebels on Tuesday.
Three people were killed and 15 wounded when a residential area was also hit, local authorities said.
The city, some distance west of the conflict zone, was the scene of major fighting until July, when pro-Russian separatists retreated.
The separatists denied firing the rockets, Reuters reports.
Kramatorsk was the scene of fierce fighting in 2014
Meanwhile Andriy Biletsky, commander of the Azov battalion based in Mariupol, confirmed to the BBC that the volunteer 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."
Rebels launched an offensive on Mariupol last month, leaving dozens dead in rocket attacks.
The Ukrainian government said that separatists appeared to be massing forces for attacks on strategic towns, including Mariupol, on Saturday, according to Reuters news agency.
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.
Government-held Mariupol is in a highly strategic position, sitting between rebel-held eastern areas and Crimea
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.
At least seven Ukrainian troops were killed overnight in the east, Ukrainian military spokesman Anatoliy Matyukhin said. In Donetsk, two civilians were killed.
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.
Rebel leaders and representatives of Russia, Ukraine and the Organization for Security and Co-operation in Europe (OSCE) are expected to meet in Minsk, the capital of Belarus, on Tuesday for talks in the run-up to the possible leaders' summit on Wednesday.
The Ukrainian ambassador to Germany said there had been "tangible results" at talks in Berlin between foreign ministry representatives of Russia, Ukraine, Germany and France on Monday.
Meanwhile German Chancellor Angela Merkel met US President Barack Obama in Washington to update him on Franco-German efforts to revive last year's Minsk peace plan, which collapsed amid fighting over the winter.
The detailed proposals have not been released but the plan is thought to include a demilitarised zone of 50-70km (30-45 miles) around the current front line.
BBC