The martial law decree gives greater powers to limit movement to, from and within the areas and allows for the residents of those territories to be moved to "safe zones."
Putin's decree to introduce military rule in the Moscow-controlled regions also gives additional power to authorities in Russian border areas and comes after a string of battlefield defeats.
"We are working on solving very complex large-scale tasks to ensure security and protect the future of Russia," Putin said.
Pro-Kremlin officials meanwhile said they were pulling out of the key southern Ukraine city of Kherson on Wednesday, as Kyiv's forces advanced on territory in Russian hands since the war's earliest days.
"The entire administration is already moving today," to the eastern bank of the Dnieper River, the Kherson region's Moscow-installed head, Vladimir Saldo, told Russian state television.
Pro-Russian officials have said civilians would only be allowed to leave towards Russia or Russian-held parts of Ukraine.
Local officials said they were planning to move up to 60,000 civilians from the city of Kherson over a period of around six days.
However, Ukrainian forces have targeted bridges across the river to disrupt supply lines so Russian-installed officials said the evacuations were being done with ferries.
Andriy Yermak, the Ukrainian presidency's chief of staff, called the moves a "propaganda show" and accused Russia of "trying to scare the people of Kherson".
Ukrainian forces "do not fire at Ukrainian cities," Yermak wrote on Telegram.
Meanwhile, Moscow has been building up its defenses in the territory it still holds.
Russia's Wagner mercenary group said it was working on building a fortified line of defense in Ukraine's eastern Lugansk region.
"It is a multi-level and layered defense," the group's founder Yevgeny Prigozhin said on the social media of his company "Concord."
Ukraine said Wednesday it had shot down 223 Iranian-made drones fielded by Moscow's forces since mid-September.
But the Kremlin has said it has no knowledge of its army using Iranian drones in Ukraine and Tehran has said the claims that it is providing Russia with weapons are "baseless".
Nabila Massrali, spokeswoman for EU foreign policy chief Josep Borrell, said the EU has "sufficient evidence" that Tehran was supplying Russia with drones and would prepare fresh sanctions on Iran.