KYIV, Ukraine (AP) – Russian troops are storming toward Ukraine’s capital, and street fighting is breaking out. The soldiers advanced Saturday as city officials urged residents to take shelter. Amid the violence, the country’s president refused an American offer to evacuate, insisting that he would stay. As dawn broke in Kyiv, it was not immediately clear how far the soldiers had advanced. Skirmishes reported on the edge of the city suggested that small Russian units were probing Ukrainian defenses to clear a path for the main forces. The street clashes followed fighting that pummeled bridges, schools and apartment buildings, and resulted in hundreds of casualties. President Volodymyr Zelenskyy is calling on Ukrainians to “stand firm” in a fight for the future of their country. U.S. defense officials believe the Russian offensive has encountered considerable resistance and is proceeding slower than Moscow had envisioned, though that could change quickly. Ukraine shot down two Russian transport planes, at least one with paratroopers on board.