The group, which has been the de facto administrator of the Gaza Strip since 2007, made threats earlier in the day to punish Israel for violent confrontations with Palestinians.
The Israeli Defense Force (IDF) sent reinforcements, closed roads and postponed a planned drill as tensions mounted. Bomb shelters opened in Ashkelon and Kiryat Melachi, which border the Gaza region.
The IDF claimed seven rockets were fired toward the capital and one was intercepted by the Iron Dome missile defense system, the Jerusalem Post reported.
An IDF spokesman said that the attacks "won’t go by quietly."
"Hamas will feel that our response to this event," said Brig. Gen. Hidai Zilberman, who labeled the events as "inexcusable." "We have a number of options on the table."
Israel responded Monday with air strikes in the Gaza Strip, killing nine Palestinians, including three children, Reuters reported. The IDF made no statement about its action.
Hamas claimed that the rocket fire was in response to Israeli "crimes and aggression against the holy city."
Palestinians and Israeli police clashed Friday at the Al-Aqsa mosque compound, a major holy site sacred to Muslims and Jews.
The Palestinian Red Crescent emergency service said 136 people were wounded in clashes with police there and elsewhere in Jerusalem, including 83 who were hospitalized.
Earlier Friday, Israeli troops shot and killed two Palestinians and wounded a third after the men opened fire on a base belonging to Israel’s paramilitary Border Police force in the occupied West Bank, the latest in a series of deadly confrontations in recent weeks that has coincided with the Muslim holy month of Ramadan.