然而，克里姆林宮發言人德米特里-佩斯科夫(Dmitry Peskov)堅持認為，在烏克蘭的軍事行動將繼續下去，"直到所有最初設定的任務 "都完成。
馬爾琴科先生說，"大約10天後"，不得不逃離該市的居民將能夠 "安全 "返回。
Ukrainian troops have seized even more territory from Russian forces as they continue their counter-offensive, the country's president has said.
Volodymyr Zelensky said troops have now retaken more than 6,000 sq km (2,317 sq miles) from Russian control since September, in the east and the south.
Russia has admitted losing key cities in the north-eastern Kharkiv region, in what is seen by some military experts as a potential breakthrough in the war.
Moscow describes its troop withdrawal in recent days as a "regrouping" with the aim of focusing on the Luhansk and Donetsk regions in Ukraine's east.
That claim has been ridiculed even in Russia, with many social media users there describing the stated pull-out as "shameful".
Speaking to the BBC on Monday evening, Mason Clark of the US-based think tank the Institute for the Study of War (ISW) said this was "a complete rout" of the Russian troops, who were forced to leave lots of equipment behind.
And the BBC's James Waterhouse said it was the most significant Russian military retreat since its failed campaign near the capital Kyiv in late March.
In his late video address on Monday, President Zelensky said: "From the beginning of September until today, our warriors have already liberated more than 6,000 sq km of the territory of Ukraine - in the east and south.
The counter-offensive - if confirmed - appears to have been rapid. Last Thursday, President Zelensky said Ukrainian forces had retaken 1,000 sq km, but by Sunday that stated figure had tripled to 3,000 sq km.
Russia's military earlier admitted that its troops had to leave the key cities of Balakliya, Izyum and Kupiansk in the Kharkiv region. Russia now controls only a small eastern part of the region.
Significant advances by Ukrainian troops have also been reported in the southern Kherson region, which borders with Crimea - a Ukrainian peninsula annexed by Russia in 2014.
However, Kremlin spokesman Dmitry Peskov has insisted that military operations in Ukraine will continue "until all the tasks that were initially set" have been fulfilled.
Valerii Marchenko, mayor of Izyum, told the BBC the Ukrainian army was in his city and the state flag had been raised.
Mr Marchenko said that after "about 10 days", residents who had to flee the city would be able to return "safely".