The general manager of Beirut's Rafik Hariri University Hospital said on Tuesday that staff would continue treating patients there despite a nearby Israeli airstrike.

"We are committed to continuing our work and will not evacuate the hospital," Dr. Jihad Saadeh said. "Although the hospital has suffered damage from shrapnel, we are prepared to treat patients in the hospital corridors if necessary."

The Lebanese Ministry of Public Health said 13 people including a child were killed and at least 57 others injured in the Israeli airstrike late Monday, with significant damage done to the nearby hospital -- the largest public medical facility in Lebanon.

There was no warning issued before the strike on the hospital, sources told ABC News. The Israel Defense Forces denied the hospital was hit and said its strike was on a nearby Hezbollah target.

Saadeh told Tuesday's press conference that some 50 healthcare centers, 150 ambulances, 150 paramedics and 15 hospitals have been targeted in Israeli attacks.

-ABC News' Josiane Hajj Moussa and Guy Davies

An Israel Defense Forces strike near Rafik Hariri Hospital in southern Beirut on Monday killed 13 people including a child and injured at least 57 others, according to the Lebanese Ministry of Public Health.

Seventeen of those injured required hospitalization, with seven in a critical condition, the ministry said in a Tuesday statement.

The hospital, which is the largest public medical facility in Lebanon, sustained significant damage, officials said.

There was no warning issued before the strike on the hospital, sources told ABC News.

The IDF denied attacking the hospital in a statement, claiming it was targeting a Hezbollah target close to the facility. "The strike did not hit the hospital and the IDF emphasizes that the hospital was not targeted, and the hospital itself and its operation were not affected," the IDF said.

-ABC News' Josiane Hajj Moussa, Jordana Miller and Guy Davies

Israel Defense Minister Yoav Gallant announced Tuesday that he designated the Al-Qard al-Hassan finance institution -- which Israel alleges is a key financial vehicle for Hezbollah -- a terrorist organization.

"Hezbollah's bank is used to purchase weapons, pay the salaries of terrorists and keep Hezbollah's terror machine going," Gallant wrote in a post on X.

"Degrading Hezbollah's capabilities requires both a military and economic campaign," he added. "We are destroying the terrorist organization's ability to both launch and buy missiles."

Israel has been targeting Al-Qard al-Hassan infrastructure throughout Lebanon in recent days. The strikes have been especially fierce in Beirut, and particularly in its southern Dahiya suburb which is known as a Hezbollah stronghold.

-ABC News' Jordana Miller

Secretary of State Antony Blinken landed at Ben Gurion Airport in Tel Aviv on Tuesday to begin a tour of Middle East nations in bid to reinvigorate cease-fire talks in both Gaza and Lebanon.

Blinken is expected to meet with Israeli Prime Minister Benjamin Netanyahu on Tuesday.

The revival of stalled cease-fire talks and the prevention of further regional escalation are at the top of the agenda for America's top diplomat.

Blinken's latest regional tour comes just two weeks to go until the U.S. presidential election and with Israel still mulling its retaliation against Iran for the latter's Oct. 1 ballistic missile attack.

-ABC News' Shannon Kingston and Guy Davies