LVIV, Ukraine - Russian missiles pounded a military base in western Ukraine on Sunday, killing 35 people in an attack on a facility that served as a crucial hub for cooperation between Ukraine and the NATO countries supporting its defense. The barrage marked an escalation of Moscow’s offensive and moved the fighting perilously close to the Polish border.

The attack so near a NATO member-country raised the specter that the alliance could be drawn into the fight and was heavy with symbolism in a conflict that has revived old Cold War rivalries and threatened to rewrite the current global security order.

More than 30 Russian cruise missiles targeted the sprawling facility, which has long been used to train Ukrainian soldiers, often with instructors from the U.S. and other countries in the Western alliance. Poland is also a transit route for Western military aid to Ukraine, and the strikes followed Moscow's threats to target those shipments.

Ukrainian President Volodymyr Zelenskyy called it a “black day," and again urged NATO leaders to establish a no-fly zone over the country, a plea that the West has said could escalate the war to a nuclear confrontation.

“If you do not close our sky, it is only a matter of time before Russian missiles fall on your territory. NATO territory. On the homes of citizens of NATO countries,” Zelenskyy said.

In addition to the fatalities, the Ukrainian Defense Ministry said that 134 people were wounded in the attack.

Ina Padi, a 40-year-old Ukrainian who crossed the border with her family, was taking shelter at a fire station in Wielkie Oczy, Poland, when she was awakened by blasts Sunday morning that made the glass in the windows shake.

“I understood in that moment, even if we are free of it, (the war) is still coming after us,” she said.

Since their invasion more than two weeks ago, Russian forces have struggled in their advance across Ukraine, in the face of stiffer than expected resistance, bolstered by Western weapons support. Instead, Russian forces have besieged several cities and pummeled them with strikes, hitting two dozen medical facilities and leading to a series of humanitarian crises.

The U.N. has recorded at least 596 civilian deaths, though it believes the true toll is much higher, and Ukraine’s Prosecutor General’s office said that at least 85 children are among them. An American filmmaker and journalist was also killed Sunday. Millions more people have fled their homes amid the largest land conflict in Europe since World War II.

Talks for a broad cease-fire have so far failed, but the Kremlin's spokesman said another round would take place on Monday by videolink, according to Russian state news agency Tass. Meanwhile, U.S. President Joe Biden is sending his national security adviser to Rome to meet with a Chinese official. There are worries in Washington that Beijing is amplifying Russian disinformation and may help Moscow evade punishing Western economic sanctions.

Zelenskyy said he will continue negotiating with Russia and making requests for a meeting with Putin, which, so far, have gone unanswered by the Kremlin. Daily talks, Zelenskyy said, were necessary to establish a cease-fire and add more humanitarian corridors, which saved more than 130,000 people in six days.

The attacked training base near Yavoriv is less than 25 kilometers (15 miles) from the Polish border and appears to be the westernmost target struck during Russia’s 18-day invasion.

U.S. Secretary of State Antony Blinken condemned the attack, tweeting: “The brutality must stop.”

The base has hosted NATO drills, and a senior official, Admiral Rob Bauer, previously hailed it as embodying “the spirit of military cooperation" between Ukraine and international forces.

As such, the site is a potent symbol of Russia's longstanding concerns that the expansion in recent years of the 30-member Western military alliance to include former Soviet states threatens its security - something NATO denies. Still, the perceived threat from NATO is central to Moscow's justifications for the war, and it has demanded Ukraine drop its ambitions to join the alliance.

Russian fighters also fired at the airport in the western city of Ivano-Frankivsk, which is less than 150 kilometers (94 miles) north of Romania and 250 kilometers (155 miles) from Hungary, two other NATO allies.

NATO said Sunday that it currently does not have any personnel in Ukraine, though the United States has increased the number of U.S. troops deployed to Poland. White House national security adviser Jake Sullivan said the West would respond if Russia's strikes travel outside Ukraine and hit any NATO members, even accidentally.

The city of Lviv, in western Ukraine itself, so far has been spared the scale of destruction happening to its east and south. Its population of 721,000 has swelled during the war, with residents escaping bombarded cities and as a waystation for the nearly 2.6 million people who have fled the country.

Ukrainian and European leaders have pushed with limited success for Russia to grant safe passage to civilians trapped by fighting. Ukrainian authorities said more than 10 humanitarian corridors would open Sunday, with agreement from Russia, including from the besieged port city of Mariupol, where the city council said 2,187 people have been killed.

But such promises have repeatedly crumbled, and there was no word late Sunday on whether people were able to use the evacuation routes. Officials did say that a convoy carrying 100 tons of aid was expected to arrive in Mariupol on Monday.

The suffering in the port city is “simply immense,” the International Committee of the Red Cross said Sunday, noting that hundreds of thousands of its residents are “facing extreme or total shortages of basic necessities like food, water and medicine.”

“Dead bodies, of civilians and combatants, remain trapped under the rubble or lying in the open where they fell,” the Geneva-based organization said in a statement. “Life-changing injuries and chronic, debilitating conditions cannot be treated.”

The fight for Mariupol is crucial because its capture could help Russia establish a land corridor to Crimea, which it seized from Ukraine in 2014.

Meanwhile, continued fighting on multiple fronts caused more misery in Ukraine on Sunday and provoked renewed international outrage.

In the southern Ukrainian city of Mykolaiv, near the Black Sea, authorities reported nine people killed in bombings. They said Russian airstrikes on a monastery and a children’s resort in the eastern Donetsk region hit spots where monks and others were sheltering, wounding 32 people.

Around the capital, Kyiv, a major political and strategic target for the invasion, fighting also intensified, with overnight shelling in the northwestern suburbs and a missile strike Sunday that destroyed a warehouse to the east.

Kyiv Region police said on its official website that Russian troops opened fire on a car carrying two American journalists. The U.S. State Department said Brent Renaud died. Juan Arredondo was wounded.

In the Kyiv suburb of Irpin, Ukrainian soldier Alexei Lipirdi, 46, said that the Russians “want to intimidate us so that we will not be calm," but he and his unit remain defiant. As he spoke, smoke billowed from distant buildings and cars stood damaged or abandoned.

The city’s mayor said only about 10,000 of its 60,000 residents remain. Many who stayed behind are the old or sick and those who are caring for them.

At a suburban hospital, doctors said 80% of their patients are civilians wounded by shelling. Patient Volodymr Adamkovych, his abdomen bandaged, said he was wounded when his home was hit. He spent the night in his basement before he could reach doctors.

By YURAS KARMANAU

Associated Press journalists from around the world contributed to this report.