"In order for the violence to stop, Hamas must stop firing rockets into Israel and agree to respect a sustainable and durable ceasefire," he said. "That is the objective to which all parties need to be working. That is what the United States is working towards."
Johndroe told reporters Hamas has "shown its true colors as a terrorist organization."
Israeli foreign minister Tzipi Livni, meanwhile, told CBS News that her country "reached last week a point in which we said enough is enough."
Livni said daily rocket fire aimed at civilians in southern Israeli towns prompted Israel to act after having "tried everything in order to avoid this military operation." She said her country's efforts did not constitute a disproportionate response.
More than 300 people have been killed in the three days of attacks, including seven children under the age of 15. Israel has vowed to continue attacking until its effort "changes the situation" on the ground.