About 14 million Ukrainians have been forced from their homes—including more than six million who have fled the country—and nearly 3,500 civilians have been killed since Russia began its invasion, United Nations officials said.

The number of people uprooted by the fighting amounts to nearly one-third of Ukraine’s prewar population of 44 million. Most of those seeking refuge outside of Ukraine are women, children or the elderly, since wartime legislation prevents most men of fighting age from leaving the country.

Millions more are effectively trapped in Ukraine, the U.N. said, estimating that 13 million people can’t leave due to heightened security risks, destroyed roads and infrastructure, and lack of resources or wherewithal to find refuge elsewhere.

Regarding the 3,496 civilian deaths, the U.N. said it believes the actual figure is far higher because the continuing battles have delayed reporting. It highlighted in particular the areas of Mariupol in the Donetsk region, Izyum in the Kharkiv region and Popasna in the Luhansk region.

The Human Rights Commissioner’s Monitoring Mission in Ukraine last week visited 14 towns and villages in the Kyiv and Chernihiv regions, which were controlled by Russian armed forces until the end of March, U.N. High Commissioner for Human Rights Michelle Bachelet said. Mission members heard firsthand accounts of relatives, neighbors and friends being killed, injured, detained and disappeared, she said.

“The scale of unlawful killings, including indicia of summary executions in areas to the north of Kyiv, is shocking,” Ms. Bachelet told a special session of the U.N. Human Rights Council in Geneva to discuss the war in Ukraine on Thursday. “Many of the allegations of violations of international human rights and humanitarian law in Ukraine may amount to war crimes.”

The U.N. Human Rights Council met in Geneva on Thursday.

Photo: fabrice coffrini/Agence France-Presse/Getty Images

A woman and her child arrived in Kyiv, Ukraine’s capital, from Poland.

Photo: sergei supinsky/Agence France-Presse/Getty Images

The U.N. expects 8.3 million people to ultimately leave the country as refugees because of the war. About half of them are expected to remain in the countries that first granted them refuge, with the rest moving elsewhere, according to the agency.

Poland, which shares a 330-mile border with Ukraine, has taken in 3.2 million people crossing the frontier—more than half of the total number of refugees—so far. Romania has taken in over 880,000.

Roughly 2.4 million refugees have now moved on from their first destination, the U.N. said. The agency also said that more than 1.59 million people have entered Ukraine since the start of the conflict. That number includes people crossing the border multiple times.

On Thursday, European Commission President Ursula von der Leyen said Russia was “the most direct threat to the world order” today. Speaking after a meeting with Japanese Prime Minister Fumio Kishida, she lashed out at what she called Russia’s “barbaric war against Ukraine.”

Ms. von der Leyen also criticized China, which has resisted Western pressure to distance itself from Moscow or condemn its invasion of Ukraine. EU relations with China were already frosty before Beijing threw political weight behind Moscow’s hostility this year. European leaders, many of whom once saw China as a counterbalance to the U.S. and Russia, now see it as more of a rival and potential threat.

A line at a Kyiv gas station.

Photo: oleg petrasyuk/Shutterstock/EPA

Russia’s “worrying pact with China and their call for ‘new’—and very much arbitrary—international relations” are a deep concern for Western-style democracies such as the EU and Japan, Ms. von der Leyen said. Alignment between Moscow and Beijing endangers “the future of a rules-based world order,” she said.

She and Mr. Kishida at their summit agreed on a range of measures on trade, digital policy and international development that they hope will strengthen ties among allies opposing policies of Moscow and Beijing.

Meanwhile, Finland’s president and prime minister on Thursday said they supported the country applying for NATO membership, making it all but certain that the Nordic nation will join the alliance in response to Russia’s invasion of Ukraine.

North Atlantic Treaty Organization Secretary-General Jens Stoltenberg said Finland would be “warmly welcomed into NATO” with a swift accession process. Ukrainian President Volodymyr Zelensky commended Finland for its “readiness to apply for NATO membership.”

Russia said Thursday it would be “forced to take retaliatory steps” if Finland became a member of the alliance.

On Wednesday, Ukraine offered to exchange Russian prisoners of war for injured fighters trapped in Mariupol’s Azovstal steel plant.

Relatives of Ukrainian service members trapped in Mariupol’s Azovstal steel plant gathered in Kyiv.

Photo: CARLOS BARRIA/REUTERS

Ukrainian servicemen attended a funeral in the Lviv region.

Photo: PAVLO PALAMARCHUK/REUTERS

Ukrainian Deputy Prime Minister Iryna Vereshchuk said the proposal calls for Russian forces to allow the removal of 38 seriously injured fighters from Azovstal via a humanitarian corridor. Russia hasn’t publicly responded.

Ms. Vereshchuk said in a social-media post on Thursday that “very difficult negotiations” were continuing.

Russia continued this week to bombard the steel plant, aiming to flush out the fighters trapped there for weeks alongside civilians seeking safe passage out of the sprawling compound.

Russia already controls the rest of the strategically vital port city after destroying most of it. Ms. Vereshchuk said on Saturday that all women, children and elderly people had been evacuated from Azovstal after a deal with U.N. backing facilitated a series of humanitarian convoys out of Mariupol to Ukrainian-controlled territory.

In another development, the governor of Russia’s Belgorod region, bordering Ukraine, said a civilian died as a result of shelling from Ukraine, the first time an official confirmed a civilian death on Russian territory since Moscow invaded its neighbor.

Vyacheslav Gladkov, governor of the Belgorod region that sits on the western edge of the country less than 20 miles from Ukraine’s war-ravaged city of Kharkiv, wrote Thursday on messaging app Telegram that a civilian had died and seven others were injured in the village of Solokhi due to shelling that originated from Ukraine on Wednesday.

Ukraine hasn’t claimed responsibility for the attack. Russia’s investigative committee said Thursday that it had ordered a criminal probe.

—Sune Engel Rasmussen and Daniel Michaels contributed to this article.

Write to Joanna Sugden at joanna.sugden@wsj.com, Matthew Luxmoore at Matthew.Luxmoore@wsj.com and Mauro Orru at mauro.orru@wsj.com