Kirill Stremousov, deputy head of the Russian-installed administration in Kherson region, said on Thursday that he hoped Russian forces would put up a fight.
With control of the Dnipro's west bank, military experts said, Ukrainian forces would have a springboard from which to seize a bridgehead on the east side for an advance on Crimea.
A U.S. official, speaking on condition of anonymity, said it appeared the Russians already had begun "an organized, phased withdrawal" from the Dnipro's west bank.
But Ukrainian troops could also face serious obstacles that could stall their takeover of Kherson, including booby traps and concentrated Russian artillery and rocket fire from the east bank, Hodges said.
The unit, with six armoured personnel carriers, took its positions in September after Ukrainian forces drove Russian troops back to Kherson's border with Mykolaiv province.