KYIV, Ukraine — Russian troops closed in on this besieged capital Friday as missiles streaked through the night, sirens wailed, the president stood defiant and civilians took up arms amid Europe’s most extensive fighting since World War II.

“Make Molotov cocktails, neutralize the occupier!” the Ukrainian Border Guard implored as tens of thousands of young and old men and women around the country loaded rifles, assembled homemade bombs and joined ragtag militias in an effort to beat back one of the most powerful armies in the world.

The battle for Kyiv unfolded into a second night as the United States and the European Union imposed some of their harshest sanctions yet against Russia while NATO, the trans-Atlantic military alliance, deployed more troops to its member states in Eastern Europe.

Despite an assessment from top Pentagon officials that Russia’s invasion was not advancing as quickly as expected thanks in part to a spirited defense by Ukraine’s air force, military and civilian deaths here were mounting and tens of thousands of refugees were fleeing. As explosions and air raid sirens sounded in the nation’s picturesque capital, a deepening awareness settled in that despite widespread global outrage over Russia’s invasion of a democratic nation, no foreign armies were coming to help.

“We are defending our country alone,” Ukrainian President Volodymyr Zelenskyy said in a solemn video address in which he ordered men of fighting age to stay in the country and arm a resistance.

Shortly after Zelenskyy spoke to President Joe Biden for nearly 40 minutes Friday, the U.S. announced new economic sanctions, this time directly against Russian President Vladimir Putin. It was the latest in a series of punishing sanctions imposed by Western powers, part of what British Prime Minister Boris Johnson called “a remorseless mission to squeeze Russia from the global economy piece by piece.”

Zelenskyy said he was grateful for the support, but he has repeatedly slammed sanctions levied against Russia as insufficient, warning that unless world leaders do more to stop the invasion, Putin would broaden his aggressions.

“If you don’t help us now, if you fail to offer a powerful assistance to Ukraine, tomorrow the war will knock on your door,” said Zelenskyy, a former comedic actor who has transformed, overnight, into a wartime leader. He called on Europeans with combat experience who were disappointed that leaders hadn’t offered more direct military assistance to come to Ukraine “and protect Europe with us.”

On the second day of its large-scale assault on Ukraine — part of Putin’s dream of stitching back together remnants of the former Soviet Union — the Kremlin sent mixed messages about whether it was open to dialogue with Ukraine in order to avert more violence.

Russian Foreign Minister Sergey Lavrov said the nation was ready for talks once the Ukrainian army laid down arms, insisting that Russia does not intend “to oppress” the Ukrainian people and said they should have “a chance to decide their future.”

But Putin was much less diplomatic at a meeting with members of his security council, where he said he did not expect to reach agreements with “a gang of drug addicts and neo-Nazis that have settled in Kyiv and taken the entire Ukrainian people hostage.”

Zelenskyy, who has repeatedly said that he would not accept a Ukraine under Russia’s thumb, has offered to negotiate on one of the Kremlin’s key demands: that Ukraine declare itself neutral and abandon its ambition of joining NATO. The goal of membership in the military alliance is enshrined in Ukraine’s constitution.

Russia’s offer of dialogue led some to question whether it had begun to doubt its ability to quickly seize control of Ukraine — or whether the conflicting messages were a part of Putin’s broader strategy of psychological warfare, not unlike his tauntingly slow buildup of tens of thousands of troops along Ukraine’s borders in recent months.

U.S. military officials said there was evidence that Russia’s attack on Ukraine, a nation the size of Texas with a population of 44 million, had not gone entirely according to plan.

A senior Pentagon official said he believed the Russians had “lost a little bit of their momentum” in their invasion, noting in a briefing to journalists that Russia had not yet captured any major Ukrainian cities or achieved air superiority over Ukraine, and that Ukraine’s communications and media systems remained intact.

The official, who spoke on the condition of anonymity, said about one-third of the roughly 190,000 troops that Russia assembled before the invasion were now in Ukraine, and that Russia had not deployed its full cyberattack capabilities.

The official said the U.S. had indications that Russia was conducting an amphibious assault west of Mariupol, on the Sea of Azov. “They are putting potentially thousands of naval infantry ashore there,” he said.

In the meantime, Russian troops continued their assault in other parts of Ukraine, hitting strategic military sites but also civilian targets.

In a Kyiv apartment building, residents woke Friday to plumes of smoke and screaming — the result, according to the city’s mayor, of Russian shelling.

“What are you doing? What is this?” asked a dazed survivor, Yurii Zhyhanov, according to The Associated Press. As tens of thousands of his compatriots have already done, he quickly gathered his belongings to flee the city with his mother.

“The enemy wants to bring the capital and us to our knees,” said Kyiv Mayor Vitaliy Klitschko, adding that Russian saboteurs had already infiltrated the city.

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