As referendums end, a declaration of Russian annexation is expected to follow.

The Russian-led referendums in occupied parts of Ukraine are expected to show that a majority of residents voted to join Russia, with the Kremlin then formally announcing annexation as soon as this week.

The voting, which has drawn broad international condemnation as rigged, concludes Tuesday in Donetsk and Luhansk in the east, and Kherson and Zaporizka in the south. If the regions are annexed, Russia has said, it would defend them as though they were Russian territory, including, potentially, with its arsenal of nuclear weapons. This strategy recalls staged votes in 2014 in Crimea that Moscow swiftly followed with annexing the peninsula.

Kremlin-backed officials began holding the referendums on Friday after a series of setbacks on the battlefield. President Vladimir V. Putin of Russia announced his support for the votes in a provocative 20-minute speech on Wednesday, adding that his top goal of the war remained “liberating” Ukraine’s eastern Donbas region.

Ukrainians have expressed fear that an immediate consequence of annexation would be conscription into the Russian military and being forced to take up arms against their own country. In parts of Luhansk and Donetsk, which have been occupied by Russia since 2014, that is already the case.

World leaders have said they would not recognize the results. Josep Borrell, the European Union’s top diplomat, said in a statement last week that the voting was “in clear violation of the U.N. Charter and Ukraine’s independence, sovereignty and territorial integrity.”

In an interview on CBS’s “60 Minutes” on Sunday, Secretary of State Antony J. Blinken said, “These so-called elections are a sham. Period.”

Jens Stoltenberg, the secretary general of the North Atlantic Treaty Organization, has called on the international community to step up support for Ukraine. “Sham referendums have no legitimacy,” he wrote on Twitter last week.