The move marks a significant escalation in violence between Palestinian militants and Israeli forces, which had been worsening in recent days.
The military said in a statement early on Friday, without providing further details, that “air and ground” troops had “begun attacking in the Gaza strip”.
Although the statement gave no further details, Israeli military affairs correspondents who are briefed regularly by the armed forces said it was not a ground invasion.
They said that troops were firing artillery from Israel’s side of the border.
Residents of northern Gaza, near the Israeli frontier, said they saw no sign of ground troops inside the enclave but reported heavy artillery fire and dozens of air strikes.
Prime Minister Benjamin Netanyahu, in an apparent reference to the operation, tweeted: “The last word was not said and this operation will continue as long as necessary.”
Israeli officials had said Hamas, Gaza’s most powerful militant group, must be dealt a strong deterring blow before any ceasefire.
Gaza militants and Israeli forces have been trading attacks for days, following a police raid at a Jerusalem mosque above a site revered by both Muslims and Jews.
The Israeli border police have been deployed in Arab and mixed Arab-Jewish cities in Israel, and more of the forces were into the streets on Thursday after another night of unrest.