Russia is pushing ahead with unilaterally annexing Ukrainian territory despite a counteroffensive that forced it to pull its troops out of an eastern logistics hub.

Russian President Vladimir Putin on Sunday submitted bills to parliament that will unite four Russian-controlled regions in eastern and southern Ukraine with Russia, as well as related ratification treaties.

Both chambers of parliament are expected to deliberate the legislation from Monday through Tuesday before Putin completes annexation procedures.

The move comes despite Ukrainian President Volodymyr Zelenskyy's announcement on Sunday that his troops have liberated Lyman, a key stronghold in the eastern region of Donetsk.

Zelenskyy also said Ukrainian forces have recaptured a number of settlements in the southern region of Kherson.

He listed the names of liberated settlements in the Kherson region in a video message released on Sunday, and said "the successes of our soldiers are not limited to Lyman."

The US-based Institute for the Study of War on Sunday released an update of its assessment of Russia's campaign. It says Russia's defeat around Lyman has caused even more confusion and negative reporting in Russia "than the Russian withdrawals from Kyiv, Snake Island or even Kharkiv."

Study of War mentions criticism of the Russian military by some of Putin's staunchest supporters, which it notes "likely publicly undermined Putin's leadership."

The British defense ministry said in its intelligence update on Monday that Putin had addressed questions over his partial military call-up that he announced on September 21.

Putin reportedly said "we must promptly correct our mistakes and not repeat them."

The ministry says "Putin's unusually rapid acknowledgement of problems highlights the dysfunction of the mobilization over its first week."

Ukraine's counteroffensive has raised speculation that it will result in both political and military setbacks for Putin's administration.