Joe Biden condemned Vladimir Putin as a “butcher” who could no longer stay in power in a historic speech in Poland as Russian missiles rained down on Ukraine’s most pro-western city, just 40 miles from the Polish border.

With explosions erupting across neighbouring Lviv, in a clear act of defiance from the Kremlin, Biden told an audience in Warsaw that the west must steel itself “for a long fight ahead”.

In what seemed to be a dramatic shift in US policy to back regime change in Moscow, Biden also appeared to urge those around the Russian president to oust him from the Kremlin. “For God’s sake, this man cannot remain in power,” Biden said in his most belligerent speech since the war began a month ago.

US officials later said that Biden had been talking about the need for Putin to lose power over Ukrainian territory and in the wider region.

The American leader said Putin was “bent on violence”. Addressing the Russian president directly, Biden said: “Don’t even think about moving on to one single inch of Nato territory.”

“There is simply no justification or provocation for Russia’s choice of war,” Biden told the audience in the Polish presidential palace.

“It’s an example of one of the oldest human impulses, using brute force and disinformation to satisfy a craving for absolute power and control. It’s nothing less than a direct challenge to the rule-based international order established since the end of world war two.”

The attacks on Lviv, the home of Ukrainian nationalism and a key player in the country’s break from the Soviet Union, bring the war directly to the European Union’s doorstep.

At least five people were injured from six missile strikes in two waves and black smoke billowed over the historic city’s horizon of steeples and cathedral domes as a fuel storage facility was hit, a mile from the Unesco-protected world heritage site. A second target was a defence facility; both were close to residential areas.

The timing of the attacks, only the third on west Ukrainian targets since the war began, and the closest to Lviv’s city centre and its residential areas, was clearly designed to send a message to the White House.

Hours earlier, Biden had met Ukraine’s defence and foreign ministers for the first time since Putin announced his “special military operation” on 24 February, and offered extra military support.

Lviv’s mayor Andriy Sadovyi said one target hit by the Russians had been “infrastructure object” and “we are putting out a fire” but declined to comment further.

Sadovyi said the explosions were a way of “saying hello to President Biden” who was in Poland. “The good thing is that nobody was killed,’ he added. Air raid sirens continued through the night sending Lviv civilians scurrying into underground shelters.

“We emerged anew in the great battle for freedom,” Biden said in his speech. “The battle between democracy and autocracy. Between liberty and repression. Between a rules-based order and one governed by brute force.

“This battle will not be won in days or months,” he added. “We need to steel ourselves for a long fight ahead.”

Referencing Pope John Paul II’s “be not afraid” speech of 1979 at the beginning and end, Biden’s speech linked the war in Ukraine with historic moments of Eastern European defiance against Soviet aggression.

“The battle for democracy did not conclude with the fall of the Berlin Wall,” Biden said. “Today Russia has strangled democracy and sought to do so elsewhere, not just in its homeland.”

Asked by reporters what seeing Ukrainian refugees at Stadion Narodowy earlier in the day had made him think of as he deals with Putin, Biden replied: “He’s a butcher.”

The Kremlin had hinted on Friday that it may be scaling back its war ambitions, saying it was close to completing the “first phase” of its military campaign and would now focus on the complete “liberation” of Donbas in eastern Ukraine. But the attacks on Lviv, 250 miles from where Biden was speaking, offered little evidence of any such plan.

Speaking to the Observer, Mykhailo Podolyak, an adviser to president Volodymyr Zelenskiy and the lead negotiator in talks with Russia, said he did not believe the Kremlin was downgrading its war aims.

“They had poor operational planning, and they realised it was advantageous for them to surround cities, cut off the main supply routes, and force people there to have a deficit of food, water and medicines,” he said, describing the siege of Mariupol as a tactic to sow psychological terror and exhaustion.

Podolyak expressed scepticism over the Russian defence ministry’s claims that Moscow’s forces would now focus mainly on the Donbas area in east Ukraine.

“Of course I don’t believe that. They don’t have interests in Donbas. Their main interests are Kyiv, Chernihiv, Kharkiv and the south – to take Mariupol, and to close the Azov Sea … we see them regrouping and preparing more troops to send in,” he said.

Podolyak later tweeted: “Lviv. Massive missile strikes. Another big Ukrainian city with great historical value. Near the border. Embassies of many countries inside the city. But the barbarians of the Russian Federation are not interested in anything – no history, no heritage, no foreign diplomas / missions. Will Europe continue to ‘pacify’?”

Earlier in the day, the Kremlin had raised the spectre of the use of nuclear weapons in the war with Ukraine as Russian forces struggled to hold a key city in the south of the country.

Dmitry Medvedev, a former Russian president who is deputy chairman of the country’s security council, said Moscow could strike against an enemy that only used conventional weapons while Vladimir Putin’s defence minster Sergei Shoigu claimed nuclear “readiness” was a priority.

The comments prompted Zelenskiy, appearing by video link at Qatar’s Doha Forum, to warn that Moscow was a direct threat to the world. “Russia is deliberating bragging they can destroy with nuclear weapons, not only a certain country but the entire planet,” he said.

Russia has about 6,000 nuclear warheads – the largest stockpile of nuclear weapons in the world. Medvedev said Russia’s nuclear doctrine did not require an enemy state to use such weapons first. Russia could use a nuclear deterrent in response to “an act of aggression committed against Russia and its allies, which jeopardised the existence of the country itself, even without the use of nuclear weapons, that is, with the use of conventional weapons.”

Shoigu, who had not been seen for 12 days before a brief appearance on Friday and an address to his generals on Saturday, also spoke about the nuclear threat contained within Russia’s arsenal. In a video, uploaded on social media by the Russian defence ministry, Shoigu said the maintenance of “engagement readiness of strategic nuclear forces” was a priority.

Meanwhile, Ukraine’s defence ministry said Russia was increasingly using undercover sabotage and reconnaissance groups in the Kyiv region after the failure to take the capital by conventional means. “The saboteurs change into civilian clothes and use cars stolen from the civilian population,” a spokesperson said.