The defiant Ukrainians rejected Russia’s demands for surrender on Monday and vowed to keep fighting in the face of indiscriminate shelling and rising death tolls as relations between Moscow and the West crumbled after the Cold War in amid outrage over “massive war crimes” committed by the Russians. President Vladimir Putin and his troops.

European Union foreign policy chief Josep Borrell has become the latest senior official to label Russia’s horrific attacks in the Ukrainian port city of Mariupol a war crime. In using such strong language, he joined President Biden, who last week called Mr Putin a “war criminal” over Russia’s seemingly indiscriminate bombing of non-military targets and acts of violence against civilians. civilians in Mariupol and elsewhere in Ukraine.

The comment prompted a severe rebuke from the Kremlin. The officials have warned that relations between the United States and Russia are “on the brink of breakdown”. Dmitry Medvedev, deputy chairman of Russia’s Security Council, said Mr Biden and other US officials are “puppeteers” seeking to drive a wedge between Moscow and the rest of the world, particularly Europe.

Mr Biden, who is due to visit Poland this week, has warned that Russia could soon launch a wave of cyberattacks against American companies. This would almost certainly trigger additional economic sanctions and other repercussions from Washington.

With the war nearly a month old, Ukrainian officials have stood firm and rejected calls to hand Mariupol over to Russian invaders. The city faced weeks of bombardment by Russian troops, resulting in countless casualties and a mass exodus of civilians. Those who remain in town have no electricity and little food and water. Russian forces seek to bombard and starve the city into submission.

Russian forces have offered the Ukrainians safe passage out of Mariupol in return for full surrender, but Ukrainian leaders have rejected the offer before a deadline in Moscow on Monday morning.

“There can be no question of any surrender” in Mariupol, said Ukrainian Deputy Prime Minister Iryna Vereshchuk.

Despite a considerable advantage in manpower and armament, the Russian invaders have yet to capture a single major Ukrainian city. Defenders are digging in Kyiv, Kharkiv and other major urban areas.

In a video address on Monday, Ukrainian President Volodymyr Zelenskyy described the aftermath of the Russian bombardment of an art school in Mariupol on Sunday. About 400 people, including children, were inside at the time. It is not known how many were killed.

Mr. Zelenskyy used the incident as a rallying cry.

“They are under the rubble, and we don’t know how many of them survived,” Mr Zelenskyy said. “But we know we will definitely shoot down the pilot who dropped that bomb, like about 100 other mass murderers we’ve already shot down.”

Mr. Zelenskyy again expressed his willingness to negotiate directly with Mr. Putin in the hope of ending the bloodshed. Ongoing negotiations between the two nations have made little progress.

In addition to the ongoing bombing campaign on Mariupol, Russian forces struck targets outside Kyiv on Monday. Heavy fighting was reported north of the city. Russian troops reportedly struck a shopping center near downtown kyiv on Sunday evening, killing at least eight people, Ukrainian emergency officials said.

Moscow said the Ukrainians were using the site as a military depot. These claims were not immediately verified.

Elsewhere, Russian troops reportedly hit civilian homes in an attack on the Black Sea city of Odessa, Ukraine’s largest port, as they continued their assault on southern Ukraine.

War of words

Bombing and rocket attacks have become Russia’s weapons of choice as its ground forces struggle to achieve their primary objectives. Western officials say Russia’s military campaign has largely stalled due to tougher-than-expected resistance from Ukrainian forces.

“The Russian forces advancing on the city from the northeast are at a standstill. Forces advancing from the direction of Hostomel to the northwest were repelled by fierce Ukrainian resistance,” the UK MoD tweeted in an analysis of the situation in Ukraine.

“Despite the continued lack of progress, kyiv remains Russia’s primary military objective and they are likely to prioritize the attempt to encircle the city over the next few weeks,” the ministry said.

US defense officials offered similar assessments, and a pro-Kremlin tabloid unexpectedly opened a window on Russian military losses so far.

In a quickly deleted online article, Komsomolskaya Pravda revealed that some 9,861 Russian soldiers had died in Ukraine and 16,153 were injured, according to recent Defense Ministry figures. Russian officials have not updated the number of casualties from the operation since March 2, when they said 498 soldiers had been killed. kyiv said nearly 15,000 Russian soldiers had been killed, but that figure could not be independently verified.

As the Russian war machine came to a standstill, its rhetorical assault on the West accelerated. Russia’s Foreign Ministry said US-Russia relations were on the brink of a major “severance” after Mr Biden’s “unacceptable statements” that Mr Putin is a war criminal.

The White House and State Department later said Mr Biden was “speaking from the heart” and not announcing a formal war crimes charge against Mr Putin. Still, US officials have said the brutal tactics of the invading Russian forces will come under scrutiny.

“We certainly see clear evidence that Russian forces are committing war crimes, and we are helping to collect the evidence,” Pentagon spokesman John Kirby told reporters. “But there are investigative processes that are going to continue, and we are going to let that happen. … As for what would come out of it, that is not a decision that the Pentagon leadership would make.

Mr. Biden is not alone in his belief.

“What is happening in Mariupol now is a massive war crime, destroying everything, bombing and killing everyone,” said Borrell, the European Union’s representative for foreign affairs and security policy.

Administration officials acknowledged last week that the US government was working with private rights groups to document Russian military operations for a possible war crimes investigation. Other NATO countries will likely participate in such an investigation.

Such close cooperation between the United States and Europe on investigations, economic sanctions and other issues has infuriated the Kremlin. The Russian Foreign Ministry summoned US Ambassador John Sullivan to complain about Mr Biden’s remarks.

“Remarks like these by the US president, which are unbecoming of such a high-ranking state figure, bring Russian-US relations to the brink of rupture,” the ministry said.

Mr Medvedev, who served as Russia’s president from 2008 to 2012, took specific aim at US ties with Poland, which has been unflinching in its opposition to Moscow even as hundreds of thousands of refugees Ukrainians cross its border and Russian rockets fall a few kilometers from its territory.

Mr Medvedev said Polish leaders sold out their people to appease the West. He specifically cited the country’s decision to stop buying Russian gas, oil and coal.

“The interests of Polish citizens are being sacrificed for Russophobia by these talentless politicians and their puppeteers across the ocean with clear signs of senility,” Medvedev said in a Telegram post.

The United States and Poland have had clear disagreements, including a dusting two weeks ago when Washington scuttled a Polish plan to deliver fighter jets to Ukraine via US military bases in Germany. US officials are rushing to arm a Warsaw proposal to form a NATO “peacekeeping” mission to deploy in Ukraine.

“The president has been very clear that we will not be sending American troops on the ground in Ukraine,” Linda Thomas-Greenfield, the US ambassador to the United Nations, told CNN over the weekend. “We don’t want to escalate into a war with the United States.”

Biden will use his visit to Poland this week to ease tensions between the countries and highlight Warsaw’s efforts to accommodate the large flows of Ukrainian refugees within its borders. The president had a call on Monday with top European leaders to discuss military and humanitarian aid to Kyiv.

Mr Biden joined a call with French President Emmanuel Macron, German Chancellor Olaf Scholz, British Prime Minister Boris Johnson and Italian Prime Minister Mario Draghi, the White House said. Biden’s trip will include meetings with NATO officials, European Union leaders and representatives of the Group of Seven’s major industrial powers.

In Washington, there were fears that Russia’s angry rhetoric was turning into action.

Mr Biden warned in a statement that “evolving intelligence” showed that “the Russian government is exploring options for potential cyberattacks” against US targets.

The statement did not specify what exactly the intelligence revealed or what the US response might be.

Mr Biden urged US companies to step up their efforts to protect themselves and said the federal government stood ready to help them fend off Russian cyberattacks.

“My administration will continue to use all tools to deter, disrupt and, if necessary, respond to cyberattacks on critical infrastructure,” he said.

• David R. Sands, Jeff Mordock and Tom Howell Jr. contributed to this article, which is based in part on Telegraph Service reports.