A day after gaining control of their first major Ukrainian city, Russian forces on Thursday laid siege to urban areas across the country in a grinding offensive that has pummeled civilian neighborhoods with increasingly heavy artillery and reduced basic services to rubble. The assaults have deepened a humanitarian crisis that has prompted 1 million people to flee the country, and 1 million more to abandon their homes for Ukrainian cities farther from the fighting.

The swift fall of the major city, Kherson in the south of the country, raised fears that other cities could soon follow as Russia’s bombardment created pressure on people to surrender. Russian forces appeared to be making their biggest gains in the south, where they had nearly surrounded two strategic cities in an apparent bid to capture Ukraine’s entire Black Sea coast, potentially cutting off the country from world shipping.

Here are the latest developments: — Russian troops have encircled the port city of Mariupol, a key point between the Russian border and the Russia-controlled Crimean Peninsula, and farther west, just north of Kherson, they were bearing down on Mykolaiv. Military experts say that capturing those cities would accomplish Moscow’s strategic objective of cutting off Ukrainian forces that have been battling Russia-backed separatists in eastern Ukraine from the rest of the country.

Russia’s advance was making less apparent progress against Kyiv, the capital, where a miles-long convoy of hundreds of military vehicles remained about 18 miles from the city center, stymied by what British intelligence officials described Thursday as “staunch Ukrainian resistance, mechanical breakdown and congestion. The United Nations said that 1 million Ukrainians had become refugees in the week since Russia launched its invasion, one of the largest exoduses in recent times. Many more have left their homes and are seeking safety in the western reaches of Ukraine or taking shelter underground.

With more and more of Ukraine cut off from reliable communications, satellite imagery provided a glimpse of the humanitarian crisis, showing people lining up outside grocery stores in parts of the country. The Kremlin forced Echo of Moscow, Russia’s flagship liberal radio station, to shut down its radio broadcast and website, in a sign of President Vladimir Putin’s rapid crackdown on dissent since the invasion. Hours later, Dozhd, Russia’s only independent general news channel, announced that it would temporarily stop broadcasting after Thursday because of a looming law criminalizing “fakes” about the war.