Both Ukrainian government forces and rebel fighters appeared to launch offensives ahead of peace talks
US President Barack Obama has warned President Vladimir Putin that Russia will face greater costs if it continues its "aggressive actions" in Ukraine.
Mr Obama urged his Russian counterpart to seize the opportunity of fresh talks to find a peaceful solution to the war that has raged since April last year.
Mr Putin is due to meet with the leaders of France, Germany and Ukraine at a summit in Belarus on Wednesday.
However, there was intense fighting in eastern Ukraine ahead of the talks.
Correspondents say both sides are attempting to make territorial gains before any possible peace agreement.
At least one person was killed and several injured when a shell hit a bus station in rebel-controlled Donetsk early on Wednesday.
On Tuesday, four soldiers and at least eight civilians were killed in rocket attacks on a key military base and a residential area in Kramatorsk.
Government officials said the rockets were fired from a rebel-held area, but separatists denied being behind the attack.
More than 5,400 people have died since the conflict began and civilian casualties have risen in recent weeks.
Ukraine and the West accuse Russia of sending troops and arms to support the rebels, but Russia denies this.
The summit in the Belarusian capital Minsk is expected to focus on securing a ceasefire and the withdrawal of heavy weapons, as well as the creation of a demilitarised zone.
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 BBC's diplomatic correspondent Bridget Kendall says it remains unclear what concessions President Putin might be prepared to make while he continues to deny Russian involvement.
President Obama phoned Mr Putin on the eve of the talks to reiterate US support for Ukraine, just days after he refused to rule out supplying "lethal defensive weapons" to Kiev if diplomacy fails.
Russia, however, has warned the West that sending arms to Ukraine would worsen the crisis.
As well as the violence in Kramatorsk, there were also renewed clashes elsewhere in eastern Ukraine.
Rebels said they had cut off the last supply route for government troops holed up in Debaltseve, a railway hub near Donetsk.
Meanwhile, 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.
- 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
- 5.2 million people estimated to be living in conflict areas
- 978,482 internally displaced people, including 119,832 children
- 600,000 fled to neighbouring countries, of whom more than 400,000 have gone to Russia