Ukrainian President Petro Poroshenko has said that Russian-backed fighters shelled the town of Kramatorsk, more than 50km from the nearest front line.
Poroshenko said the first round of rocket fire hit the headquarters of the Ukrainian command in eastern Ukraine and the second landed in a residential area.
The government-controlled Donetsk regional administration said 12 people were killed and 64 wounded, including 29 civilians.
Rebels denied any involvement in the attack and said it was a "provocation" by the Ukrainian authorities.
Kramatorsk was the site of major fighting until July, when pro-Russian separatists retreated.
Fighting has intensified across eastern Ukraine ahead of much-anticipated peace talks, involving Western leaders, set to take place in Minsk, the Belarus capital, on Wednesday.
Ukraine's Azov battalion, loyal to Kiev, also announced it would be launching an offensive against the Donetsk city of Novoazovsk.
The battalion said later on social media on Tuesday that it had captured several villages northeast of the strategic port of Mariupol, pushing the rebels back closer to the border with Russia.
However, rebel military spokesman Eduard Basurin said in a televised news conference that the rebels had not retreated.
Azov said the rebels had shelled the village of Kominternove, east of government-controlled Mariupol, causing unspecified civilian casualties.
A reporter for the AP news agency at a government checkpoint between there and Mariupol was told of ongoing fighting several miles away.
Rebels 'surround Debaltseve'
Earlier on Tuesday, pro-Russia separatists in eastern Ukraine said they had completely surrounded the strategic town of Debaltseve, a claim denied by the Ukrainian army who insisted that the fighting is ongoing.
The self-proclaimed Donetsk People's Republic (DPR) said its fighters had cut off the main supply road into the government-held town - which is in between the separatist hubs of Luhansk and Donetsk.
The route had also been used as a humanitarian corridor in recent weeks, allowing civilians to flee the fighting.
Al Jazeera's Charles Stratford, reporting from the nearby town of Yanovka, spoke to a separatist military commander who supported the rebels' claims.
The commander said that Debaltseve was completely surrounded by separatists.
"As he [the commander] understands it the separatists are not in the town, the Ukrainian military are still inside," Stratford said.
"The military are denying this, saying there are ongoing battles on the main supply route out of the city. We were on that supply route yesterday and the Ukrainian military we saw were in a state of disarray.
"They wanted us out immediately and were pulling back their heavy weaponry. The situation is very fluid and there is no direct contact with the separatist fighters."
Major rail hub
Debaltseve is of great strategic importance to both sides in the conflict as it is the site of a major rail hub that connects the DPR with Russia.
"We have spoken to separatist commanders in recent weeks and they have said they are not interested in pushing for peace until they have taken the town," our correspondent said.
"There is a greater sense of confidence now among the separatists, whereas the general atmosphere among the Ukrainian troops is one of panic, especially on that main supply route."
Separatist fighters from the DPR urged Ukrainian forces to surrender and leave Debaltseve peacefully, said rebel spokesman Basurin.
"We guarantee security to all who lay down their arms. The others will be eliminated," Basurin said.
"If the enemy attempts to attack in another place, the strike will be repelled. Some 5,000 - 6,000 Ukrainian servicemen have been trapped in Debaltseve."
Source: Al Jazeera and agencies