Russian-backed officials are calling on Putin to annex Ukrainian regions after referendums that were widely dismissed as a sham.

Kyiv, Ukraine Russian representatives in the occupied areas of Ukraine on Wednesday appealed to President Vladimir V. Putin to join Russia, kicking off what is expected to be several days of pomp and paperwork aimed at giving Russia’s annexation plans a gloss of legitimacy.

The moves are intended to check the boxes under Russian law and the Russian constitution in a process to reclaim land in a neighboring country that most of the rest of the world considers patently illegal.

Organized referendums in occupied areas of Ukraine were hastily launched last week after Russia suffered battlefield setbacks. After five days of rigged voting, in which many residents said armed soldiers forced them to vote, Russian representatives in the occupied areas announced so-called results showing, as expected, overwhelming support for joining Russia.

With the results apparent in hand, the proxies called on the Russian government to incorporate their territories into Russia in informal calls issued Wednesday morning.

The goal is to declare parts of Ukraine as Russian territory and then claim that the Ukrainian military is attacking Russia, and not the other way around. Annexation would also provide a pretext to recruit Ukrainian men in occupied areas and force them to fight other Ukrainians.

The Russian military controls only parts of the four provinces and has been losing ground. But if Russia follows the pattern set to annex Ukraine’s Crimean peninsula in 2014, the Kremlin will present military-installed local leaders as independent actors. In that case, he followed a carefully choreographed multi-step process.

Putin could stop the process at any stage, possibly to open up negotiating prospects with the threat of annexation clearly on the table. If he does not, the next step would be to present the appeals of the Russian deputy leaders for approval by both houses of the Russian Parliament. There would be few surprises here: both chambers are made up entirely of members loyal to Putin.

In two of the four provinces that in recent days held voting demonstrations in referendums to join Russia Donetsk and Lugansk Moscow established client states eight years ago. Kicking off the annexation process, the leaders of these entities left for Moscow on Wednesday and said they would speak directly with Putin.

In two others, Zaporizhzhia and Kherson, puppet leaders on Wednesday declared independence from Ukraine in what they said was a first step toward being absorbed into Russia, a necessary formality since, under Russia’s 1993 constitution, Moscow cannot annex areas of a neighboring country without the country’s consent.

Denis Pushilin, the leader of the Donetsk People’s Republic, said he was leaving for Moscow with a document signed by members of an electoral commission showing the results for use in the annexation process, Tass, the Russian news agency, reported. The leader of the Luhansk People’s Republic, Leonid Pasechnik, was also reported to be on his way to Moscow and posted a video online asking Putin to accept what he called the election results.

In the Kherson region of southern Ukraine, the leader established by the Russian occupation army last spring, Volodymyr Saldo, also publicly appealed to Putin to consider accepting Kherson as part of Russia.

Until now, Putin has been coy about his plans. His spokesman, Dmitri S. Peskov, said Putin traveled from the Black Sea resort of Sochi to Moscow on Wednesday but did not plan to comment publicly on the referendums.