Donetsk Governor Vadim Filashkin said more than 53,000 people, including 4,000 children, remain in the city.
He said authorities decided to forcibly evacuate the children and their parents or guardians.
“When our city is virtually within range of all enemy weapons, the decision to evacuate becomes necessary and inevitable.”
Mr Dobriak said the number of people evacuating from the village had increased to 500 to 600 per day. He said basic services in the village were still operating but that they were likely to be disrupted soon as Russian troops advanced.
The evacuation order came as Ukrainian President Volodymyr Zelensky said his troops were continuing their victories in the Russian-occupied Kursk region.
President Zelensky said the invasion was “achieving its goals,” adding that more Russian prisoners of war were being added to what he called an “exchange fund.”
One of the goals of the invasion was reportedly to divert Russian troops from the Donbass region, thereby relieving pressure on the Ukrainian military there, which is in crisis.
On Monday, Russian military bloggers claimed that Ukraine had blown up a third bridge over the Seymour River in the Kursk region. Kiev has not claimed responsibility, but the destruction of the bridge would likely further hamper Russian military logistics and help Ukraine tighten its grip on territory it has seized from Moscow.
But BBC Verify has spotted a new pontoon bridge across the river. Pontoon bridges are temporary, floating bridges that are quickly built and used in situations where there is no permanent structure, and they appear to have been built by the Russian military.
Satellite images taken on Saturday show two recently built intersections near Glushkovo.
