Ukrainian rebels say they have agreed to a take part in further peace talks in Donetsk on Friday.
It comes as a ceasefire declared by the Ukrainian government was due to expire on Thursday.
Both the rebels and the government accuse each other of breaking the ceasefire.
Heavy shelling overnight on Wednesday in Slovyansk destroyed houses, and electricity shortages cut off water supplies for many.
One woman whose house was damaged said: “In our neighbourhood there has been shooting for about a week. This is the third time that it has been so bad. Yesterday it was very bad. It was very close. We were all sitting here.”
Eighteen people have been killed since the ceasefire was declared last Friday
Ukraine’s prime minister, Arseniy Yatsenyuk, said the country was facing a new type of conflict.
“The situation in the country is too difficult. Unplanned billions are being spent on ensuring the territorial integrity of Ukraine as a state. There is a new form of war being waged against us,” he said.
Public pressure is growing in Ukraine for a response to the downing of a military helicopter on Tuesday which killed nine soldiers.