Trump says damage to Iran's nuclear sites is 'far below ground level'

The International Atomic Energy Agency is monitoring the situation in Iran "very carefully," the body's Director General Rafael Grossi told the IAEA's board of governors on Monday.

The IAEA is watching Iran's nuclear facilities and the level of radiation "through constant communication with Iranian authorities," Rossi said in a statement published on the IAEA website.

The agency, he added, is ready to respond to an emergency within an hour and will remain present in Iran. Grossi said he is in touch with inspectors on the ground and "stands ready to travel immediately."

Grossi also provided a status update on Iran's three key nuclear facilities -- the fuel enrichment plants at Natanz and Fordow plus the Isfahan nuclear site.

Grossis said there had been no additional damage at Natanz since Israel's opening strikes on Friday, which destroyed the above-ground part of the pilot fuel enrichment plant and electrical infrastructure.

The level of radioactivity remains unchanged and at normal levels outside the Natanz site, but within the facility "there is both radiological and chemical contamination," Grossi said.

Grossi reported that four buildings had been damaged at Isfahan, but that off-site radiation levels remained unchanged.

The IAEA chief said there was no damage at Fordow.

-ABC News' Charlotte Gardiner

The Israeli military said Monday it had achieved "full aerial operational control above Tehran."

Israeli Defense Forces spokesperson Brigadier General Effie Defrin also said that the Israeli military had destroyed one third of Iran's surface-to-surface missile launchers, which Tehran has been using to fire ballistic missiles toward Israel.

-ABC News' Dana Savir, Jordana Miller and Ellie Kaufman

U.S. Ambassador to Israel Mike Huckabee reported "some minor damage" to the American Embassy branch office in Tel Aviv on Sunday night due to "concussions of Iranian missile hits" nearby.

Huckabee said there were no injuries among U.S. personnel. American diplomatic offices in Israel remain closed alongside a shelter in place order for U.S. personnel.

Following a spate of missile strikes from Iran into Israel on Monday morning, local time, Israeli Emergency Services said medical teams have confirmed three people were killed and over 70 others were injured. Two women and one man, all approximately 70 years old, were killed, officials said. A 30-year-old woman is in serious condition and five others are in moderate condition. The remaining injuries were mild, officials said.

Israeli Fire and Rescue services reported damage to two buildings in Tel Aviv and additional damage to a building in the Central District, in Petah Tikva.

-ABC News' Will Gretsky