Russian forces launched a deadly attack on the town of Kostyantynivka in eastern Ukraine on Sunday, hours after Ukraine’s leader decried Russia’s assumption of the United Nations Security Council presidency given its ongoing aggression.

Six people were killed and eight were wounded when “massive shelling” hit Kostyantynivka, according to Andriy Yermak, a top adviser to President Volodymyr Zelensky of Ukraine. In a post on the Telegram messaging app, he added that 16 apartment buildings were damaged, along with private homes, a pre-school and other buildings in the industrial town. The claims could not be independently verified.

Kostyantynivka is about 15 miles from the city of Bakhmut, where Ukrainian forces have been locked in a brutal, monthslong battle to fend off Russian troops. Mr. Zelensky stopped in the town late last month as part of a morale-boosting tour to thank soldiers involved in the defense of Bakhmut.

The attack there on Sunday drove home Mr. Zelensky’s furious response to Russia’s assumption of the Security Council Presidency, which he said was “obviously absurd and destructive.”

Russia is scheduled on Monday to preside over a Security Council meeting for the first time since it began the full-scale war in Ukraine almost 14 months ago. The Security Council aims to maintain international peace and security, and the role of the presidency is a largely ceremonial one, taken for a month at a time in alphabetical order by each of the council’s 15 members.

It has come to Moscow weeks after President Vladimir V. Putin was accused of war crimes by the International Criminal Court. The situation is a reminder that Ukraine and its allies, most notably the United States and Europe, have not always been successful in isolating Russia economically and politically to punish the Kremlin for the war.

Three of the Security Council’s 15 current members — China, India and the United Arab Emirates — have avoided openly blaming Russia for the war, instead calling for both sides to cease hostilities. Ukraine is not a current member, but Mr. Zelensky implored those countries to change tack.

“It is important when the states that are neutral in the military-political sense nevertheless take a clear moral position towards Russian terror, towards Russia’s destruction of the global order based on rules,” Mr. Zelensky said.

Western officials have said that there is no legal path for removing Russia from its permanent seat at the Security Council, which set up Moscow’s presidency for the month of April. While Russia will not hold increased influence during its term in the presidency, it will manage the agenda for meetings.

Ukrainian officials say more than 450 children are among the thousands of civilians who have been killed in the war and almost twice as many wounded. They also accuse Russia of forcibly moving almost 20,000 Ukrainian children to its territory.

Last week, Ukraine’s allies announced that they would task the Organization for Security and Co-operation in Europe, an intergovernmental group, to formally investigate the widespread reports of forced child deportations, which also formed a key part of the International Criminal Court’s accusations against Russia.

“This crime committed by Russia is one of the most cynical and anti-human crimes of our time,” Mr. Zelensky said.

Russian officials were unfazed by the criticism over its assumption of the Security Council presidency. Dmitry Polyanskiy, a deputy Russian ambassador to the United Nations, said his country would act as an “honest broker.”

“Any attempts to provoke us are doomed to fail in advance,” he said on Saturday, according to the Russian news agency Tass.

The baby invoked by Mr. Zelensky died in a Russian attack on Avdiivka, a town in Ukraine’s east that has recently been subjected to increased bombardment. Russian troops have been engaged in a weekslong offensive across a broad front in eastern Ukraine. On Saturday, they continued their attacks, targeting areas around Lyman, Bakhmut and Avdiivka, according to Ukrainian officials.

In Avdiivka and Druzhkivka, another town in the eastern Donetsk region, Russia fired ballistic missiles at civilian targets, the General Staff of the Armed Forces of Ukraine said in its morning update early Sunday. It said the attacks caused civilian casualties. The reports could not be independently confirmed.

“Having no desired results on the battlefield, the enemy continues to cynically wage war against civilians,” the Ukrainian update said.