MOSCOW - Russian proxy officials in occupied areas of Ukraine have appealed to Vladimir Putin, the Russian president, to annex the regions. The appeals followed sham referendums in four regions in Ukraine that purported to put a stamp of approval on joining Russia. Many of the ballots were cast at the point of a gun, witnesses said.

The formality of the annexation requests was at odds with the chaos Russia faces both on the battlefield, where it continues to suffer losses, and at home, where tens of thousands are fleeing the country to avoid a military draft. It came as the E.U. moved to impose new sanctions on Russia, including an oil price cap, trade restrictions and blacklisting of individuals who were responsible for the referendums.

When it comes to annexation, Russian officials appear to want at least a patina of legality — even as most of the world condemns the referendums, and Russia’s land grab, as patently unlawful. Under Russia’s 1993 Constitution, Moscow cannot annex areas of a neighboring country without consent.

In phone calls to friends and relatives at home, Russian soldiers gave damning insider accounts of battlefield failures and civilian executions, excoriating their leaders just weeks into the campaign to take Kyiv.