New peace push offers clues to fundamental question: What does Putin want?

The plan, which has been revised since it was leaked last week, drew pushback from Ukraine and its supporters in Congress and Europe for hewing to Moscow’s uncompromising vision for a postwar settlement. Still, Putin has shown little interest in signing it.

On Thursday, he described the proposal as a list of questions—each one requiring hard work to resolve—and he made one of his most explicit demands yet for the territory that has been at the center of negotiations.

“When Ukrainian troops leave the territories they hold, then the fighting will stop," Putin said. “If they don’t, then we’ll achieve that through military means."

Ukraine has vowed to never cede territory to Russia. But the problem for Ukraine and many of its Western backers is that Russia’s stated goals extend far beyond conquering eastern Ukraine—an impression that was only reinforced by elements of the 28-point plan.

Putin’s statements suggest that ultimately the Russian leader wants to deprive Ukraine of its sovereignty, restore Moscow’s influence over Kyiv and roll back the North Atlantic Treaty Organization’s encroachment into a region that Russia sees as its sphere of influence. That would mean any agreement that doesn’t satisfy Putin’s core objectives would likely be a prelude to a new invasion aimed at securing them.

“Anything that prevents a future war is unacceptable for Putin," said Russian economist Konstantin Sonin, a professor at the University of Chicago Harris School of Public Policy. “There is no future for Russia which does not involve continuing to fight for Ukraine until Ukraine is fully integrated into Russia."

The 28-point plan was revised this week after senior Trump administration officials met with Ukrainian and European officials in Geneva. White House special envoy Steve Witkoff is expected to travel to Moscow next week for another round of negotiations.

Witkoff drafted the plan with input from Kremlin confidant Kirill Dmitriev. A transcript of a call published by Bloomberg News this week showed Witkoff advised a top Kremlin aide, Yuri Ushakov, on how Putin should approach a conversation with Trump.

In the call, Witkoff suggested to Ushakov that territory in eastern Ukraine might be the key to unlocking a peace deal. “Me to you, I know what it’s going to take to get a peace deal done. Donetsk and maybe a land swap somewhere," he said.

The plan Witkoff drafted called for limiting the size of Ukraine’s military, blocking its path to joining NATO and prohibiting the alliance’s troops from stepping foot on Kyiv’s territory. But Putin’s own words indicate Moscow is interested in much more.

Putin has often referred to the “root causes" of the conflict. He invokes centurieslong historical grievances to justify the invasion and advance claims that any moves by Kyiv toward the West are a historical aberration.

In essays and speeches throughout his quarter-century rule, Putin has described modern Ukraine as an artificial construct created by early Soviet leaders and said Ukrainians and Russians are one people. In an essay he published in July 2021, which was made mandatory reading for all Russian soldiers and is now seen as the prelude to his invasion of Ukraine the following year, he lamented Ukraine’s drift away from Russia and promised to reverse it.

“The formation of an ethnically pure Ukrainian state, aggressive toward Russia, is comparable in its consequences to the use of weapons of mass destruction against us," he wrote.

Putin describes Ukraine as part of a single “historical and spiritual space" with Russia. In a February 2022 speech announcing the invasion, he said Ukraine had been hijacked by hostile forces intent on wiping out the Russian speakers living in its eastern provinces. He singled out the diminishing influence of the Russian-backed Orthodox Church in Ukraine.

The 28-point plan would oblige Ukraine to adopt rules on the protection of linguistic minorities and religious tolerance, a clear nod to Putin’s complaints. It would also compel Kyiv to roll back many restrictions placed on the use of Russian in public spaces.

Prominent Russian figures have helped broadcast Putin’s narrative, among them Alexander Dugin, whom some call “Putin’s brain" because he long promoted ideas Putin ultimately adopted.

In a recent post on Telegram, Dugin described work under way for “mass treatment and psychological rehabilitation" of Ukrainians. “Ukraine will be entirely ours within at most two years—quite possibly much sooner," Dugin wrote on Telegram on Sunday. “There will no longer be even the slightest trace of sovereignty there, since Ukrainians are absolutely incapable of using it."

A draft treaty the Kremlin drew up with Ukrainian officials in Istanbul in the spring of 2022, which was ultimately not agreed upon, provided a clue to the concessions Russia might try to force from Ukraine if Western military support dries up and Moscow’s forces continue to make significant territorial gains.

That draft treaty, which Putin has cited as a starting point for talks, included a ban on heavy weaponry for Ukraine and would render it a “permanently neutral state that doesn’t participate in military blocs." It capped its armed forces at 85,000 troops, less than 10% of its current strength, and set limits on its long-range weapons. The newly modified U.S. initiative caps the military at 800,000 and includes no restriction on missiles.

There are provisions in the U.S.-backed proposal—such as ceding all of the Donbas region in eastern Ukraine and assurances that Ukraine won’t host foreign troops on its soil—that could make the deal palatable to Putin.

Putin is signaling that if Russia’s battlefield advance continues, he won’t need to win Ukrainian-held territory through diplomacy because his forces will eventually seize it. His generals have been inflating their successes on the battlefield in Ukraine’s east, where they now appear poised to take two large cities. Armed-forces chief Valery Gerasimov told Putin during a meeting with top officers last week that Russia is advancing across all fronts and has seized the city of Kupyansk, even though Ukraine still partially controls it.

“If the developments we witnessed in Kupyansk unfold in other areas, the collapse of the front will be inevitable," Putin said in comments about the U.S. peace plan on Thursday, arguing that Ukraine and Europe were hobbling the efforts.

Western officials say more than 250,000 Russian soldiers have died fighting in Ukraine, but generous army salaries and a pervasive narrative of sacrifice have blunted the societal impact of those losses.

Ultimately, analysts say, Putin is hoping to clinch a grand geopolitical bargain that secures his control over Ukraine—dealing with the U.S. over the heads of European and Ukrainian officials. Sergey Radchenko, a Russian historian and professor of history at Johns Hopkins School of Advanced International Studies, compares the current moment with the post-World War II period when Joseph Stalin, in Yalta, sought U.S. agreement to divide Europe into spheres of influence.

“If you think of the future of Ukraine as being decided effectively by the United States and Russia, bypassing the Europeans, you can see the outlines of Yalta in that," Radchenko said.

Write to Matthew Luxmoore at matthew.luxmoore@wsj.com