Local militiaman Valery, 37, carries a child as he helps a fleeing family across a bridge destroyed by artillery, on the outskirts of Kyiv, Ukraine, Wednesday, March 2. 2022. Russian forces have escalated their attacks on crowded cities in what Ukraine's leader called a blatant campaign of terror. Photo: AP/Emilio Morenatti)

The escalation of attacks on crowded cities followed an initial round of talks between outgunned Ukraine and nuclear power Russia on Monday that resulted in only a promise to meet again. It was not clear when new talks might take place — or what they would yield. Ukraine’s leader earlier said Russia must stop bombing before another meeting.

Seven days into the war, roughly 874,000 people have fled Ukraine and the U.N. refugee agency warned the number could cross the 1 million mark soon. The overall death toll was not clear, but Ukraine’s State Emergency Service said more than 2,000 civilians have died. It was impossible to verify that claim.

Countless others have taken shelter underground, as Russia continued its bombardment.

Another attack came Wednesday on Kharkiv, a city with a population of about 1.5 million, and a reported strike on a hospital in the country’s north. A 40-mile (64-kilometer) convoy of hundreds of Russian tanks and other vehicles advanced slowly the capital of Kyiv, while Russian forces pressed their assault on the strategic southern city of Kherson.

Russian President Vladimir Putin’s goals are not clear, but the West has warned he may be seeking to topple the government and install a Kremlin-friendly regime.

Ukrainian President Volodymyr Zelenskyy has decried Russia’s attacks on civilian targets as a blatant terror campaign, while U.S. President Joe Biden warned on Tuesday that if the Russian leader didn’t “pay a price” for the invasion, the aggression wouldn’t stop with one country.

A Russian strike hit the regional police and intelligence headquarters in Kharkiv, killing four people and wounding several, the state emergency service of Ukraine said. It added that residential buildings were also hit, but did not provide further details.

A blast blew the roof off of the five-story police building and set the top floor alight, according to videos and photos released by the service. Pieces of the building were strewn across adjacent streets.

In the northern city of Chernihiv, two cruise missiles hit a hospital, according to the Ukrainian UNIAN news agency, which quoted the health administration chief. Serhiy Pivovar said and authorities were working to determine the casualty toll.

The attacks followed a day after one in Kharkiv’s central square that shocked many Ukrainians for hitting at the center of life in a major city. A Russian strike also targeted a TV tower in the capital of Kyiv on Tuesday — and caused damage at the nearby site of the Babi Yar Holocaust memorial.