According to Israel's military, "precise attacks" are being carried out in Dahieh, the densely populated suburb of Beirut that has been subjected to extensive Israeli attacks recently and where the Shia militia Hezbollah has a strong presence. A Hezbollah intelligence officer has been killed in the attack, according to Israel.
In the same area, Hezbollah's leader Hassan Nasrallah was killed during extensive bombing on Friday evening.
In Lebanon, more than 30 people have been killed and up to 200 injured in Israeli attacks on Saturday, according to the Lebanese Health Department.
Sources, including the AFP news agency, report that a warehouse located near Lebanon's only international airport has been hit by an Israeli attack.
Earlier on Saturday, sirens sounded over central Israel. According to Israel's military, this was after a rocket was fired from Yemen. However, the rocket was shot down outside the country's borders, the military reports.
The Iran-backed Houthi movement in Yemen has claimed responsibility for the attack.
According to a statement, the group had Israel's Ben Gurion Airport outside Tel Aviv in its sights, at the same time as Israel's Prime Minister Benjamin Netanyahu was due to land there after his trip to the UN General Assembly in New York, AP reports.
Hezbollah has also carried out attacks during the day. According to Israeli reports, up to a hundred rockets have been fired at mainly northern Israel, but also more central parts of the country, from Lebanon.