Seven Ukrainian troops are said to have died in a clash with pro-Russian rebels near Donetsk airport.
The attack is the deadliest single incident for the military since a truce deal.
A tank shell hit the vehicle carrying the troops, an official said.
Three civilians were reportedly killed in other incidents.
Ukrainian activists earlier toppled a statue of Lenin in the eastern city of Kharkiv – a move likely to be seen as a provocation by pro-Russians.
Nationalist protesters had gathered around the statue on Sunday night for a “Kharkiv is Ukraine” rally. The governor of Kharkiv region, Ihor Baluta, then signed an order to dismantle the statue.
The mayor of Kharkiv, Gennady Kernes, said on a local government website that the monument would be restored, calling its destruction unlawful.
Pro-Russian demonstrators defended the statue in February, as similar monuments were being taken down in other parts of the country in a wave of protests that accompanied the removal of President Viktor Yanukovych.
Kharkiv has largely escaped the violence which subsequently swept through east Ukraine’s other regions, Donetsk and Luhansk.
The latest deaths cast fresh doubt on a ceasefire agreed between the Ukrainian government and the rebels on September 5.
The seven soldiers were killed in a vehicle near Donetsk airport, which the rebels have been trying to capture from the Ukrainian military.
“During the evening attack, the Ukrainian armoured transporter, with its crew and a paratroop unit, took a direct hit from a tank,” Ukrainian military spokesman Col Andriy Lysenko told reporters.
He said a total of nine soldiers had been killed and 27 wounded in the past 24 hours.
Separately, authorities in Donetsk told AFP news agency that three civilians had been killed over the same period. The city is a base for the pro-Russian rebels.
The OSCE, which is monitoring the ceasefire, confirmed there had been heavy shelling around Donetsk airport.
For several days Russian state television has reported on “mass graves” allegedly unearthed by rebels near Nizhnya Krynka, a village near Donetsk. At least four bodies have been found there, according to the Russian reports.
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