Is Russia pulling back to regroup?

 ISW:

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The Kremlin's claimed withdrawal of forces around Kyiv, which it seeks to portray as a “huge step” towards peace, is a cover for an ongoing redeployment of Russian forces after their failure to take Kyiv. Russian Deputy Defense Minister Colonel-General Alexander Fomin claimed on March 29 that Russia will “drastically reduce military activity in the Kyiv and Chernihiv directions” and provide details on Russia’s claimed withdrawal later this week.[1] Chief Russian negotiator Vladimir Medinsky falsely framed this claimed withdrawal as a “huge step” toward peace that requires “counter-movement” from Ukraine.[2] The Kremlin is attempting to falsely portray the failure of its campaign to encircle Kyiv, which ISW assessed had failed as of March 19, as an olive branch requiring a Ukrainian concession.[3] Russian forces continue to fight to hold their front-line trace near the city, and Russian forces have been withdrawing into Belarus for rest and refit for several days – prior to the Russian announcement on March 29.[4] Russia’s redeployment of forces to other fronts and continued shelling around Kyiv are not concessions and should not be treated as such by Ukraine and its partners.

Kyiv remained firm that Ukraine must receive separate security guarantees if it abandons its NATO aspirations. Ukrainian officials called for the establishment of a security guarantee system for Ukraine (involving Russia, China, the United States, Germany, Turkey, the United Kingdom, and France) if Ukraine drops its NATO aspirations.[5] None of those countries have publicly committed to such a system and are unlikely to do so; Kyiv will therefore likely refuse Russian demands to commit to not joining NATO.

Ukraine's delegation offered possible limited concessions on territorial control but stated all Russian forces must withdraw prior to any territorial negotiations. Ukraine’s delegation presented an agreement stating Ukraine would not join NATO, would adopt a neutral status, and would not host foreign forces if Russia provided security guarantees and withdrew all its forces from Ukraine. Ukraine also offered a fifteen-year negotiation period on the future of the Russian-occupied Crimean Peninsula.[6] Zelensky emphasized in a March 27 interview with Russian media that Russia should return its forces to the positions they held before the February 24 invasion prior to any dialogue on control over the Donbas.[7] Zelensky left open the possibility of conceding parts of eastern Ukraine, emphasizing that “Ukrainian land is important, yes, but ultimately, it's just a territory,” but also said that Ukraine would not compromise Ukrainian territory without “iron-clad” security guarantees.[8] Ukrainian Presidential Advisor Mykhailo Podolyak said on March 29 that Ukraine will sign an international agreement on security guarantees only after holding a national referendum on the issue.

The Kremlin said Ukraine’s proposal was “clearly formulated” after previously falsely claiming Kyiv refused to provide a firm position and stated the Kremlin will consider Kyiv’s proposal before responding. Medinsky stated on March 29 that Russia proposed to “expedite” plans to schedule a meeting between Zelensky and Putin to occur prior to the conclusion of negations.[9] Medinsky stated Russia’s delegation will pass Ukraine’s “clearly formulated position” to President Putin, after which Moscow will give a response, but did not specify a timeline for further meetings.
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It does appear that Russia realizes how exposed its troops are near Kyiv.  They are probably still having logistic problems keeping them in food and fuel while also being vulnerable to Ukraine counterattacks.  It is also not clear that if they stayed there they would have sufficient combat force to attack Kyiv. Even if they try to stand off and hit Kyiv with artillery and rockets, they still have the problem of keeping them in ammo over a treacherous supply line. Right now their negotiating leverage is their occupation even if they are too weak to attack.

Russia is also having to deal with internal opposition that it is trying to suppress.

See, also:

Russian Army Begins to Withdraw From Kiev to Russia and a Lot of Folks Are Very Unhappy With the Pig in the Poke They Were Sold