Latest Ukraine-Russia War News: Live Updates From Mariupol

Those who had been trapped in Mariupol outside the steel mill described a fragile existence, subsisting on Russian rations cooked outside on wood fires amid daily shelling that left corpses lying in debris.

Yelena Gibert, a psychologist who reached Ukrainian-held territory with her teenage son on Monday, described “hopelessness and despair” in Mariupol, and said residents were “starting to talk of suicide because they’re stuck in this situation.”

Heavy fighting in the eastern Donetsk and Luhansk regions has yielded minimal gains for the forces of President Vladimir V. Putin of Russia, Western officials say. But the Russians continued to fire rockets and shells at Ukrainian military positions, cities, towns and infrastructure along a 300-mile-long front, including bombarding the Azovstal plant, where the last remaining Ukrainian fighters in Mariupol are hunkered down.

On Monday, Ukraine said it had used Turkish-made drones to destroy two Russian patrol vessels off the Black Sea port of Odesa, just before Russian missiles struck the city, causing an unknown number of casualties and damage to a religious building.

The U.S. State Department said that Russia’s war aims now include annexing Donetsk and Luhansk — partially controlled before the Feb. 24 invasion by Russia-backed separatists — as soon as mid-May, and possibly the southern Kherson region as well.

“We believe that the Kremlin may try to hold sham referenda to try to add a veneer of democratic or electoral legitimacy, and this is straight out of the Kremlin’s playbook,” Michael Carpenter, the U.S. ambassador to the Organization for Security and Cooperation in Europe, told reporters at a State Department briefing in Washington.

As the war drags on and evidence of atrocities mounts, the West’s appetite has grown for retaliation that would have been rejected out of hand a few months ago. The U.S. Senate is preparing to take up President Biden’s $33 billion aid package for Ukraine, including a significant increase in heavy weaponry, and the European Union is expected this week to impose an embargo on Russian oil, a significant step for a bloc whose members have long depended on Russian energy.

House Speaker Nancy Pelosi, days after becoming the highest-ranking U.S. official to visit Kyiv since the war began, met in Warsaw with President Andrzej Duda of Poland on Monday, in an effort to strengthen Washington’s partnership with a key NATO ally that has absorbed millions of Ukrainian refugees and helped funnel arms to the battlefield.

Ms. Pelosi called for the “strongest possible military response, the strongest sanctions” to punish Russia for the invasion, despite Moscow’s threats of retaliation against the West. “They have already delivered on their threat that killed children and families, civilians and the rest,” she said.

More than two months into the invasion, Russia is struggling to capture and hold territory, according to a senior Pentagon official who briefed reporters on background to discuss intelligence. The official called Russia’s latest offensive in eastern Ukraine, the region known as Donbas, “very cautious, very tepid” and, in some cases, “anemic.”

“We see minimal progress at best,” the official said on Monday, citing incremental Russian advances in towns and villages. “They’ll move in, declare victory, then withdraw their troops, only to let the Ukrainians take it.”

Britain’s defense intelligence agency said that of the 120 battalion tactical groups Russia had used during the war — roughly 65 percent of its entire ground combat forces — more than a quarter had likely been “rendered combat ineffective.”

Some of Russia’s most elite units, including its Airborne Forces, have “suffered the highest levels of attrition,” the British assessment said, adding that it would “probably take years for Russia to reconstitute these forces.”

As the fighting…