In a move swiftly dismissed by Ukraine, Russian-controlled regions of eastern and southern Ukraine announced plans Tuesday to start voting on the question of becoming integral parts of Russia. The quickening Kremlin-backed efforts to swallow up four regions could set the stage for Moscow to escalate the war following Ukrainian successes on the battlefield. They could also invite a ratcheting up of Ukrainian counterattacks.

The scheduling of referendums starting Friday in the Luhansk, Kherson, and partly Russian-controlled Zaporizhzhia and Donetsk regions came after a close ally of President Putin said the votes are needed and as Moscow is losing ground in the invasion it began nearly seven months ago, increasing pressure on the Kremlin for a stiff response.

A former president, Dmitry Medvedev, the deputy head of Russia’s Security Council chaired by Mr. Putin, said referendums that fold regions into Russia itself would make redrawn borders “irreversible” and enable Moscow to use “any means” to defend them.

The votes, in territory Russia already controls, are all but certain to go Moscow’s way but are unlikely to be recognized by Western governments that are backing Ukraine with military and other support.

There are also indications that Ukraine will attempt to undercut Russia’s referendum schemes by military means. Last Friday, Ukrainian forces lobbed a volley of American-made Himars rockets at Russia’s provisional military-civilian headquarters at the strategic port city of Kherson, scoring a direct hit. The likelihood of additional attacks may have accelerated Moscow’s fresh push for the annexation votes. 

Ukraine’s southern military command said today that  its troops sank a Russian barge carrying troops and weapons across the Dnieper River near the city of Nova Kakhovka. It offered no other details on that  attack, which took place in the Russian-occupied Kherson region.

The Ukrainian foreign minister, Dmytro Kuleba, quickly denounced the referendums as a sham and tweeted, “Ukraine has every right to liberate its territories and will keep liberating them whatever Russia has to say.”

There was also swift international condemnation. Speaking in New York, where he is attending the UN General Assembly, the German chancellor, Olaf Scholz, said: “It is very, very clear that these sham referendums cannot be accepted.” Latvia’s foreign minister, Edgars Rinkevics, called for more sanctions against Russia and more weapons for Ukraine, tweeting: “We must say no to Russian blackmail.”

In Donetsk, part of Ukraine’s wider Donbas region that has been gripped by rebel fighting since 2014 and that Mr. Putin has set as a primary objective of the invasion, the separatist leader, Denis Pushilin, said the vote will “restore historic justice’ to the territory’s “long-suffering people.” They “have earned the right to be part of the great country that they always considered their motherland,” he said.

In partly Russian-occupied Zaporizhzhia, a pro-Russia activist, Vladimir Rogov, said: “The faster we become part of Russia, the sooner peace will come.” Pressure inside Russia for votes and from Moscow-backed leaders in Ukrainian regions that Moscow controls increased after a Ukrainian counteroffensive — bolstered by Western-supplied weaponry — that has recaptured large areas.

A former Kremlin speechwriter and Russian political analyst, Abbas Gallyamov, said on Facebook that Moscow-backed separatists appeared “scared that the Russians will abandon them” amid the Ukrainian offensive and forged ahead with referendum plans to force the Kremlin’s hand.

The Kremlin spokesman, Dmitry Peskov, said there are no prospects for a diplomatic settlement. Mr. Medvedev, who served as Russia’s president between 2008 and 2012, said on his messaging app channel that separatist region votes are important to protect their residents and would “completely change” Russia’s future trajectory.

“After they are held and the new territories are taken into Russia’s fold, a geopolitical transformation of the world will become irreversible,” Mr. Medvedev said in the message, which would appear to confirm that the votes will be bogus.

A Ukrainian analyst, Volodymyr Fesenko, head of the independent Penta Center think-tank based in Kyiv, said the Kremlin hopes the votes and the possibility of military escalation will raise the pressure from Western governments for President Zelensky to start talks with Moscow.

The move “reflects the weakness, not the strength of the Kremlin, which is struggling to find levers to influence the situation that has increasingly spun out of its control,” he said.

The recapturing of territory, most notably in the northeastern Kharkiv region, has strengthened Ukraine’s arguments that its troops could deliver more defeats to Russia with additional armament deliveries.

More heavy weaponry is on its way, with Slovenia promising 28 tanks and Germany pledging four additional self-propelled howitzers. More aid also is expected from Britain, already one of Ukraine’s biggest military backers after America. Prime Minister Truss is expected to promise that in 2023, her government will “match or exceed” the $2.7 billion in military aid given to Ukraine this year.