Ukraine is hitting Russia hard in the regions Moscow is trying to seize

(CNN) -- As Vladimir Putin lost more of the Ukrainian territory he is seeking to annex, his government on Tuesday sought to finalize the formalities of its claim to four Ukrainian regions, none of which are fully controlled by Russia anymore.

The upper house of Russia's rubber-stamp legislature, the Federation Council, on Tuesday unanimously approved the decision to annex the Ukrainian regions of Donetsk, Kherson, Luhansk and Zaporizhzhia in defiance of international law and a day after the lower chamber had done the same. President Putin was expected to sign the legislation later in the day, his spokesman said.

Kyiv's military, however, has continued to advance into several of the areas Russia now claims as its own, spurring questions about whether the Kremlin can hold the parts of those territories it currently controls -- and even what Russia would consider its new border after the annexation. Kremlin spokesman Dmitry Peskov said Monday that Moscow needed to "continue consulting" with the local populations before establishing its boundaries.

How Russia plans to take the four regions it has sought to claim as its own remains unclear, at least in the short-term. Peskov hinted last week that Russia will attempt to retake the territory at a later date, and that campaign will likely involve some of the 300,000 reservists being called up as part of a "partial mobilization" ordered by Putin last month.

Russian Defense Minister Sergei Shoigu said Tuesday more than 200,000 people have joined the country's military since the announcement, which sparked protests and sent hundreds of thousands of people -- mostly fighting-age men -- fleeing into neighboring countries.

For now, Ukrainian forces are continuing to push ahead with their surprisingly successful counteroffensive that has seen, as one Ukrainian official put it Tuesday, more areas liberated "every day."

On Sunday, Kyiv took control of Lyman, an important logistical railway hub in Donetsk that the Russian army used to funnel troops and supplies to the west and south. The Russian Defense Ministry said it was forced to cede Lyman or risk encirclement of its troops there, allowing Ukrainian forces to potentially use the city as a staging post to push troops further east.

The victory at Lyman was followed by Ukrainian gains in Luhansk on Monday and success in the push south toward Kherson overnight Monday into Tuesday, which saw Kyiv retake the towns of Davydiv Brid and Velyka Oleksandrivka.

"Ukrainian marines are confidently advancing towards the Black Sea," Ukraine's Defense Ministry tweeted Tuesday as it announced the gains in Kherson.

Donetsk and Luhansk are both in eastern Ukraine, and fighting against Moscow-backed breakaway republics in each region has been raging since 2014. Kherson and Zaporizhzhia are in southern Ukraine and have been occupied by Russian forces since shortly after the invasion began in late February.

Kyiv's recent success has not been lost on those in the Kremlin. Pro-Russian bloggers and propagandists have been unusually critical of the war effort in recent days. Though there were no votes against annexation in parliament, one senator aired concerns Tuesday that Russia would be absorbing territory "occupied by the armed forces of another country."

With defeats piling up, changes appear to be in store for the Russian war machine. Records show the Kremlin recently removed Col. Gen. Alexander Zhuravlyov as head of the Western Military District, one of five such districts in the country's military and a key player in the war in Ukraine.

US officials have voiced concerns that Putin may escalate the conflict in response to Ukraine's battlefield success. Washington is considering how to respond to a range of potential scenarios, including if Russia were to use tactical nuclear weapons, according to three sources briefed on the latest intelligence. Officials caution the US has not detected preparations for a nuclear strike.

The US and many of the world's developed democracies have continually voiced strong opposition to the entire annexation process, including the so-called referendums held in the four regions Russia is attempting to annex. Those staged contests, which purportedly showed the majority of people living there wanted to join Russia, were widely panned as a farce that failed to meet internationally recognized standards of free and fair elections. Reports from the ground suggested that voting took place both essentially and literally at gunpoint.

The results were followed by a fiery speech from Putin at the Kremlin's St. George's Hall on Friday. In the address, Putin announced that the regions would be annexed and the millions of people living in there would be Russian citizens "forever." On Tuesday, Russia's deputy foreign said residents would have one month to change their citizenship.

Members of the G7 -- Canada, France, Germany, Italy, Japan, the United Kingdom and the United States -- and the European Union responded by saying they would never recognize the Kremlin's sovereignty over the regions and vowing to "impose further economic costs on Russia."

Western leaders have continued to unveil new sanctions on Putin's regime in recent days. The UK government on Tuesday sanctioned the leader of the Kherson region for "destabilizing Ukraine or undermining or threatening the territorial integrity, sovereignty or independence of Ukraine."

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