The rebels have accused the Ukrainian army of shelling and bombing the village of Luhanska.
But Ukrainian officials said their forces were not in the area, blaming the rebels themselves.
Hundreds of people have been killed since a pro-Russian rebellion began in eastern Ukraine.
A shaky ceasefire ended on Monday. President Petro Poroshenko had called the 10-day unilateral ceasefire, which rebel leaders later joined, but ended it as both sides accused each other of violations.
Diplomatic moves to renew the truce were stepped up on Wednesday as the German foreign minister hosted talks in Berlin with his Ukrainian, Russian and French counterparts.
"Only when the guns fall silent, only on the basis of a robust ceasefire, are negotiations on resolving the crisis imaginable," Frank-Walter Steinmeier said before the meeting.
Five soldiers were killed and 28 wounded in rebel attacks in Donetsk region on Tuesday, the government said.
The civilian deaths came in the early hours of Wednesday, when several buildings were reportedly hit in the village of Luhanska.
Amateur videos were posted on YouTube showing ruined buildings and bodies on a street.
Neither the reports of casualties nor the videos could be verified independently.
According to the rebel leadership in Luhansk, government forces attacked the village with artillery and from the air, killing 10 people on a single street.
The situation was the same in another village, Nova Kondrashivka, a statement said, although there was no confirmation.
However, Ukrainian security forces in the region were quoted by Interfax news agency as saying the rebels had attacked the village themselves, at around 04:00 (01:00 GMT), causing deaths and damage.
While there had been artillery shelling in the area, it was "completely in the opposition direction".
Ukrainian officials said on Facebook that no air force planes had been operating there at the time, although that statement was disputed by someone claiming to be a witness.
The rebels in Donetsk said separately that two of their fighters had been killed in fighting on Wednesday at Nikolayevka.
They also reported that three members of the same family had been killed in the Kramatorsk-Sloviansk area (Donetsk) by government shelling.
Troops stationed above the rebel stronghold of Slavyansk fought off rebel attempts to break out of the encirclement, the government said, but lost one soldier killed and 10 wounded.
In another development, a Su-25 ground attack jet crashed at Dnipropetrovsk airport, reportedly after mechanical failure.
The pilot ejected to safety.
Mr Steinmeier was meeting Russian Foreign Minister Sergei Lavrov, France's Laurent Fabius and Ukraine's Pavlo Klimkin.
A French diplomatic source told Reuters news agency: "It's an opportunity to work on peace efforts but we don't want to raise expectations."
The violence erupted in eastern Ukraine in April as separatists declared independence in the Donetsk and Luhansk regions.
Russia annexed the Ukrainian region of Crimea in March.
The crisis was triggered last November, when Ukraine's President Viktor Yanukovych, decided not to sign an EU deal last year - under pressure from Russia - leading to protests in Kiev and his eventual overthrow.
President Poroshenko signed the free trade part of the EU deal in Brussels last Friday, after earlier signing the political co-operation clauses.
Source: BBC News Europe