KYIV, Ukraine • Ukraine said Tuesday that Russia seemed to soften its stand in the talks aimed at halting the fighting, even as Moscow’s forces stepped up their bombardment of Kyiv, smashing apartments, a subway station and other civilian sites.

Elsewhere around the country, civilians in at least 2,000 cars fled Mariupol along a humanitarian corridor in what was believed to be the biggest evacuation yet from the desperately besieged seaport, where bodies have had to be buried in mass graves.

Also, the leaders of three European Union countries — including Poland, a NATO member on Ukraine’s doorstep — visited the embattled capital in a bold show of support amid the danger.

The talks between Russian and Ukrainian representatives, with the latest round held Tuesday via video, have become “more constructive,” and Russia has stopped airing its demands for Ukraine to surrender, said Ukrainian presidential aide Ihor Zhovkva.

Zhovkva said that Ukrainian representatives felt “moderately optimistic” after the talks, adding that it would be necessary for Ukrainian President Volodymyr Zelensky and Russia’s Vladimir Putin to meet to make major progress.

With the number of people driven from the country by the war eclipsing 3 million, large explosions thundered across Kyiv before dawn from what Ukrainian authorities said were artillery strikes, as Russia’s assault on the capital appeared to become more systematic and edged closer to the city center.

Zelensky said barrages hit four multistory buildings in the city and killed dozens of people.

The shelling ignited a huge fire in a 15-story apartment building and spurred a frantic rescue effort.

The strikes, carried out of the 20th day of Russia’s invasion, targeted a western district of Kyiv, disrupting a relative calm that returned after an initial advance by Moscow’s forces was stopped in the early days of the war.

A senior U.S. defense official, speaking condition of anonymity to discuss the Pentagon’s assessment, said the Russians were using long-range fire to hit civilian targets within Kyiv with increasing frequency but that their ground forces were making little to no progress around the country.

The official said Russian troops were still about 9 miles from the center of Kyiv.

The official said the U.S. has seen indications that Russia believes it may need more troops or supplies than it has on hand in Ukraine, and it is considering ways to get more resources into the country. The official did not elaborate.

Before Tuesday’s talks commenced, Ukrainian presidential aide Mykhailo Podolyak said they planned to discuss a cease-fire and Russian troop withdrawal.

Russian Foreign Minister Sergey Lavrov said Moscow would press its demands that Ukraine drop its bid to join NATO, adopt a neutral status and “demilitarize.”

In a statement that seemed to signal potential grounds for agreement with Moscow, Zelensky told European leaders gathered in London that he realizes NATO has no intention of accepting Ukraine.

“We have heard for many years about the open doors, but we also heard that we can’t enter those doors,” he said. “This is the truth, and we have simply to accept it as it is.”

NATO does not admit nations with unsettled territorial conflicts. Zelensky has repeatedly said over recent weeks that he realizes NATO isn’t going to offer membership to Ukraine and that he could consider a neutral status for his country but needs strong security guarantees from both the West and Russia.

The U.N. said close to 700 civilians in Ukraine have been confirmed killed, with the true figure probably much higher.

People who fled the war in Ukraine leave Przemysl train station Tuesday in Przemysl, Poland.

the associated press