Fierce battles resumed in the past three days around the ruins of the airport in eastern Ukraine, said spokesman Andriy Lysenko.
The airport is under government control and has been a flashpoint for clashes with pro-Russian rebels who hold the city.
Lysenko said there were no precise details yet on the number of casualties at the airport.
It was not immediately clear if the three soldiers were killed at the airport or elsewhere in the conflict zone.
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Meanwhile, artillery shells damaged around a dozen sites overnight in Donetsk.
AFP journalists reported a residential building was badly damaged. City authorities put the number of injured at 14.
Fighting in Ukraine's east between government forces and pro-Russian rebels has killed over 4,300 people and displaced 930,000 since it broke out in April.