KYIV, Ukraine—Street fighting broke out early Sunday in Kharkiv as Russian troops pushed into Ukraine’s second-largest city, according to a regional official, following a wave of attacks elsewhere targeting airfields and fuel facilities that appeared to mark a new phase of an invasion that has been slowed by fierce resistance. The U.S. and EU responded with weapons and ammunition for the outnumbered Ukrainians and powerful sanctions intended to further isolate Moscow. Russian troops approached Kharkiv, about 20 kilometers (12.4 miles) south of the border with Russia, shortly after Moscow launched its invasion of Ukraine on Thursday. But until Sunday, they remained on the outskirts of the city of 1.4 million without trying to enter while other forces rolled past, pressing their offensive deeper into Ukraine. Early Sunday, Russian troops moved in and were engaged by Ukrainian forces, said Oleh Sinehubov, the head of the Kharkiv regional administration, who told civilians not to leave their …