LVIV, Ukraine (AP) — Besieged Ukrainians held out hope Monday that renewed diplomatic talks with Moscow might open the way for more civilians to evacuate, as Russian forces kept up their pressure on the capital, the day after escalating the offensive by shelling areas close to the Polish border.

Overnight, Russian forces fired artillery on suburbs northwest of Kyiv, a major political and strategic target for the invasion, as well as points east of the city, regional administration chief Oleksiy Kuleba said on Ukrainian television.

A town councilor for Brovary, east of Kyiv, was killed in fighting there and shells fell on the towns of Irpen, Bucha and Hostomel, which have seen some of the worst fighting in Russia’s stalled attempt to take the capital, Kuleba said.

Artillery hit a nine-story apartment building in a northern district of the city early Monday morning, destroying apartments on several floors and igniting a fire. The state emergency agency, which released images of the smoking building, said it had no immediate reports of casualties.

The general staff of Ukraine’s armed forces said Monday morning that Russian troops have not made major advances over the past 24 hours, despite expanding strikes to the west.

In one such attack, 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. It raised the possibility that the alliance could be drawn into the fight. The attack was also heavy with symbolism in a conflict that has revived old Cold War rivalries and threatened to rewrite the current global security order.

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, urging Russian President Vladimir Putin to meet with him directly, a request that has gone unanswered by the Kremlin.

A fourth round of talks is expected Monday between Ukrainian and Russian officials via video conference to discuss getting aid to cities and towns under fire, among other issues, Ukrainian presidential aide Mykhailo Podolyak said.

The talks will involve the same higher-level officials who met earlier in Belarus, aimed at “assessing preliminary results” of talks so far, Podolyak said. Previous talks have not led to major breakthroughs or a solution for getting aid or evacuation convoys to the desperate, strategic city of Mariupol.

Meanwhile, President Joe Biden is sending his national security adviser to Rome to meet with a Chinese official over worries that Beijing is amplifying Russian disinformation and may help Mosc ow evade Western economic sanctions.

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. Millions more people have fled their homes amid the largest land conflict in Europe since World War II.

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 creating a series of humanitarian crises.

That fight expanded Sunday to the sprawling facility at Yavoriv, which has long been used to train Ukrainian soldiers, often with instructors from the United States and other countries in the Western alliance. More than 30 Russian cruise missiles targeted the site. In addition to the fatalities, the Ukrainian Defense Ministry said 134 people were wounded in the attack.

The base 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. It has hosted NATO training drills, making it a potent symbol of Russia’s longstanding fears that the expansion 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.

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 shook her windows.

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

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.

Ukrainian and European leaders have pushed with limited success for Russia to grant safe passage to civilians trapped by fighting. Ukrainian authorities said Sunday that more than 10 humanitarian corridors were set to open, including from the besieged port city of Mariupol. But such promises have repeatedly crumbled, and there was no word late Sunday on whether people were able to use the evacuation routes.

The International Committee of the Red Cross said suffering in Mariupol was “simply immense” and that hundreds of thousands of people faced extreme shortages of food, water and medicine.

“Dead bodies, of civilians and combatants, remain trapped under the rubble or lying in the open where they fell,” the Red Cross 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.