There was no immediate comment on the incident by Israel or by Hezbollah.
Lebanese authorities and Hezbollah have both endorsed a ceasefire as a means to end the conflict, but diplomats fear that diplomacy has taken a back seat to military operations.
Lebanon's acting U.N. Ambassador Hadi Hachem told the council that "only diplomatic solutions and the implementation of international resolutions, the commitment to international law and international humanitarian law is the means to end this war and this aggression."
Israel did say it had killed Muhammad Abdullah, the head of the Islamic Jihad's network in the Palestinian refugee camp of Nur Shams in the West Bank. The Palestinian health ministry said on Friday that two people were killed in an Israeli strike on Nur Sham.
Abdullah, who Israel said had been involved in a number of attacks against its soldiers, was killed along with another "terrorist" in a strike near Tulkarm, the military and security agency said in a statement on Friday.
The United Nations' peacekeeping force in Lebanon, UNIFIL, said two of its personnel were injured when an Israeli tank fired at a watchtower on Thursday at its main headquarters in Naqoura, hitting the tower and causing the peacekeepers to fall.
The two peacekeepers were from Indonesia's contingent and were in good condition after being treated for light injuries, Indonesia Foreign Minister Retno Marsudi said in a statement.
The safety of more than 10,400 U.N. peacekeepers in Lebanon is
"increasingly in jeopardy" and operations have virtually halted since late September, U.N. peacekeeping chief Jean-Pierre Lacroix told the Security Council. That coincides with Israel's escalation of its conflict with Lebanon.
UNIFIL called attacks on peacekeepers "a grave violation of international humanitarian law."
The White House said the U.S. was deeply concerned by reports that Israeli forces fired on U.N. positions and was pressing Israel for details.
Israel's military said in a statement its troops operated in the Naqoura area, "next to a UNIFIL base."
"Accordingly, the IDF instructed the U.N. forces in the area to remain in protected spaces, following which the forces opened fire in the area," Israel's statement said, adding it maintains routine communication with UNIFIL.
The peacekeepers are determined to
remain at their posts despite Israeli attacks and orders by Israel's military to leave, the force's spokesperson Andrea Tenenti said.
In New York, Israel's U.N. Ambassador Danny Danon said Israel recommends UNIFIL relocate 5 km (3 miles) north "to avoid danger as fighting intensifies".
Danon said attacking Hezbollah was necessary so 70,000 displaced Israelis could return to homes in northern Israel.
The Middle East remains on high alert for further escalation in the region, awaiting Israel's response to an
Iranian missile strike on Oct. 1.
U.S. vice president and Democratic presidential candidate Kamala Harris said de-escalation was needed.
"We have got to reach a ceasefire," Harris told reporters as she departed Las Vegas, while commenting on the situations in Gaza and Lebanon. "We've got to de-escalate."
A ceasefire remains elusive in Gaza and Lebanon. Washington's occasional condemnation of Israel over civilian deaths has mostly been verbal with no substantive change in policy.