Ukrainians on Friday braced for a violent battle for their capital, Kyiv, as officials warned residents to stay indoors and “prepare Molotov cocktails” to defend against advancing Russian forces who had entered a northern district of the city.

As missile strikes hammered Kyiv and a rocket crashed into a residential building, Moscow made clear that its goal is to topple the government of President Volodymyr Zelensky. He, in turn, urged Ukrainians in a televised address to defend the country, saying that no foreign troops were coming to their aid. Here is what else is happening in the Russian attack.

Mr. Zelensky said that 137 Ukrainian soldiers and civilians had been killed in the Russian invasion that began on Thursday. The United Nations reported a lower tally of casualties but said that any figures were probably an undercount.