Russia's military forces kept up their punishing campaign to capture Ukraine's capital with fighting and artillery fire in Kyiv's suburbs Monday after an airstrike on a military base near the Polish border brought the war dangerously close to NATO's doorstep.

Residents of besieged Ukrainian cities held out hope that renewed diplomatic talks might open the way for more civilians to evacuate or emergency supplies to reach areas where food, water and medicine are running short.

Air raid alerts sounded in cities and towns all around the country overnight, from near the Russian border in the east to the Carpathian Mountains in the west, as fighting continued on the outskirts of Kyiv. Ukrainian officials said Russian forces shelled several suburbs of the capital, a major political and strategic target for an invasion in its 19th day.

Two people died after artillery hit a nine-story apartment building in a northern district of the city, according to Anton Gerashchenko, an adviser to Ukraine’s Interior Ministry. Using a ladder, a group of firefighters painstakingly carried an injured woman on a stretcher away from the blackened and still smoking building.

Also read: Russian airstrike escalates offensive in western Ukraine

A town councilor for Brovary, east of Kyiv, was killed in fighting there, officials said.

Shells also fell on the Kyiv suburbs of Irpin, Bucha and Hostomel, which have seen some of the worst fighting in Russia’s stalled attempt to take the capital, regional administration chief Oleksiy Kuleba said on Ukrainian television.

A fourth round of talks is expected Monday between Ukrainian and Russian officials to discuss getting food, water, medicine and other desperately needed supplies to cities and towns under fire, among other issues, Ukrainian presidential aide Mykhailo Podolyak said.

The surrounded southern city of Mariupol, where the war has produced some of the greatest human suffering, remains cut off despite earlier talks on creating aid or evacuation convoys.

It will be a “hard discussion,” Podolyak wrote on Twitter. “Although Russia realizes the nonsense of its aggressive actions, it still has a delusion that 19 days of violence against (Ukrainian) peaceful cities is the right strategy.”

The hope for a breakthrough came the day after Russian missiles pounded a military training base in western Ukraine that previously served as a crucial hub for cooperation between Ukraine and NATO.

The attack killed 35 people, Ukrainian officials said, and the base's proximity to the borders of Poland and other NATO members raised concerns that the Western military alliance could be drawn into the the largest land conflict in Europe since World War II.

Speaking Sunday night, Ukrainian President Volodymyr Zelenskyy called it a “black day,” and again urged NATO leaders to establish a no-fly zone over his 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.

The president's office reported Monday that airstrikes hit residential buildings near the important southern city of Mykolaiv, as well as in the eastern city of Kharkiv, and knocked out a television tower in the Rivne region in the northwest. Explosions rang out overnight around the Russian-occupied Black Sea port of Kherson.

Three airstrikes hit the northern city of Chernihiv overnight, and most of the town is without heat. Several areas haven’t had electricity in days. Utility workers are trying to restore power but frequently come under shelling.

Also read: Ukraine says 85 children killed since invasion

The government announced plans for new humanitarian aid and evacuation corridors, although ongoing shelling caused similar efforts to fail in the last week.

Despite Russia's punishing assault on multiple fronts, Moscow's troops did not make major advances over the past 24 hours, the general staff of Ukraine’s armed forces said Monday morning. The Russian Defense Ministry gave a different assessment, saying its forces had advanced 11 kilometers (7 miles) and reached five towns north of Mariupol.

A defense ministry spokesman said Russian forces shot down four Ukrainian drones overnight, including a Bayraktar drone. Ukraine’s Bayraktar drones, made by NATO member Turkey, have become a symbol of Russian President Vladimir Putin’s accusations that the U.S. and its allies pose an existential security threat to Russia.

U.S. 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 since Russia invaded Ukraine on Feb. 24, though it believes the true toll is much higher. The Ukrainian prosecutor general’s office said the death toll includes at least 85 children are among them. Millions more people have fled their homes.

While Russia's military is bigger and better equipped than Ukraine's, Russian troops have faced stiffer than expected resistance, bolstered by Western weapons support. With their advance slowed in several areas, they have bombarded several cities with unrelenting shelling, hitting two dozen medical facilities and creating a series of humanitarian crises.

The International Committee of the Red Cross said suffering in Mariupol, where missiles struck a maternity hospital Wednesday, 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. But after invading Ukraine from Crimea and two other directions, Moscow has waged a multi-pronged attack and encircled several cities.

The assault expanded Sunday to the International Center for Peacekeeping and Security near Yavoriv, a military base which has long been used to train Ukrainian soldiers, often with instructors from the United States and other NATO members. More than 30 Russian cruise missiles targeted the site. In addition to the 35 deaths, 134 people were wounded in the attack, the Ukrainian Defense Ministry said.

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.

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.

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.

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 from across the border 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.