Smoke rises amid damaged buildings following an attack on the Yavoriv military base in Lviv, Ukraine. Reuters

Diplomatic efforts to end the war in Ukraine were stepping up on Monday, with Ukrainian and Russian negotiators set to talk again after both sides cited progress, a day after Moscow escalated its offensive by shelling areas perilously close to the Polish border.

Besieged Ukrainians held out hope on Monday that renewed diplomatic talks with Russia might open the way for more civilians to evacuate, even after Russia attacked a base near the Polish border and fighting raged elsewhere.

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Ukraine's leader warned that the attacks could expand to neighbouring countries.

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.

Displaced Ukrainians onboard a Poland bound train in Lviv, western Ukraine, on Sunday. AP

A barrage of Russian missiles hit Ukraine's Yavoriv International Centre for Peacekeeping and Security, a base just 15 miles (25 km) from the Polish border that has previously hosted NATO military instructors, killing 35 people and wounding 134, a Ukrainian official said on Sunday.

Russia's defence ministry said up to 180 "foreign mercenaries" and a large number of foreign weapons were destroyed. Reuters could not independently verify the casualties reported by either side.

Thousands of people have died since Feb 24, when Russian President Vladimir Putin launched what he called a special military operation to rid Ukraine of dangerous nationalists and Nazis.

Ukrainian President Volodymyr Zelensky 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.

Ukrainian President Volodymyr Zelensky stands during a video address on Saturday. AFP

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

Diplomats were due to resume talks on Monday, according to Russian state news agency Tass. Meanwhile, US 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 UN 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.

Kate, who fled Ukraine, reads a story to her daughter Dianna in a refugee centre in Korczowa, Poland. AP

That fight expanded on 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 Defence Ministry said 134 people were wounded in the attack.

The base is less than 25 kilometres (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.