The White House says the apparent abduction of an Israeli soldier would be an "absolutely outrageous" action by Hamas.
Deputy National Security Adviser Tony Blinken says the US strongly condemns the alleged abduction. He says that if the soldier has been kidnapped, he must be released.
The Israeli military says one of its soldiers is "feared" abducted, but has not provided further details. The report came as a ceasefire with Hamas collapsed just hours after it took effect.
Thirty-five Palestinians were also killed by Israeli shelling.
Blinken said Secretary of State John Kerry was speaking to Israeli prime minister Benjamin Netanyahu about the unravelling ceasefire.