“They have, at this time, told us that those are limited operations focused on Hezbollah infrastructure near the border, but we’re in continuous conversations with them about it,” spokesperson Matthew Miller said at a press briefing as quoted by CNN.

Israel said on Saturday it killed Hezbollah leader Sayyed Hassan Nasrallah in an airstrike on Beirut's southern suburbs, escalating tensions across the Middle East.

Describing Nasrallah as "one of the greatest enemies of the State of Israel," the Israeli military claimed that his elimination "makes the world a safer place."

The Israeli military confirmed that Nasrallah, who led Hezbollah for 32 years, was killed in Friday's airstrike in Beirut, the stronghold of the Iran-backed group. Hezbollah confirmed his death on Saturday.

Israeli Prime Minister Benjamin Netanyahu said Nasrallah’s death was retribution for the killing of Israelis and other foreign nationals, including Americans. He added that had Nasrallah survived, he would have rapidly rebuilt Hezbollah’s operational strength.

U.S. President Joe Biden called Nasrallah's death a "measure of justice," reasserting the stance of the U.S., which supplies arms to Israel.

More than one million people across Lebanon have been uprooted by ongoing and deadly Israeli airstrikes across the country, including one reported early Monday morning in a residential area of central Beirut, adding to fears of a full-scale invasion.

In a situation update published on Monday the World Health Organization (WHO) reported that 11 health workers had been killed and 10 injured between 17 and 28 September. Some 37 health centres have been forced to close due to the fighting out of 317 in total, and three hospitals treating patients have been evacuated.

“Many healthcare workers have been displaced especially in the south, Bekaa and South Beirut”, WHO reported.

WHO is continued to support Lebanon’s public health emergency response with staffing, financial and technical support, helping coordinate referrals and boosting trauma surgery capacity.

Meanwhile, some 100,000 of the displaced have reached neighbouring Syria, according to the UN refugee agency, UNHCR.

“The outflow continues,” said UN High Commissioner for Refugees, Filippo Grandi, in a tweet, accompanied by a picture of hundreds of people squeezed together at a Syrian-Lebanese border crossing.

Grandi noted that the agency’s teams were on hand at four crossing points inside Syria to support new arrivals.

The development follows a dramatic escalation of hostilities between the Israel military and the Hezbollah armed group based in Lebanon, whose longtime leader Hassan Nasrallah was killed in a strike on Friday.

On Monday, Hamas announced that its leader in Lebanon, Fatah Sherif al-Amin, had been killed in an airstrike on a refugee camp for Palestinians, along with his family.

Humanitarian relief is being provided by the refugee agency, UNHCR and other UN agencies including UNRWA, the UN agency for Palestine refugees, which has opened nine shelters accommodating 3,350 people.

“UNRWA provides in these shelters aid based on impartiality and non-discrimination, hosting Palestine refugees, Lebanese and Syrian refugees, supporting all in need,” said UNRWA Lebanon spokesperson Fadi El Tayyar.

The UN aid coordinating office, OCHA, said that 90 per cent of the one million people displaced fled their homes in just the last week.

“Displacement now surpasses the 2006 war, triggered by intense Israeli strikes and orders for civilian evacuations,” said OCHA in a tweet.

According to Lebanon’s health ministry, Israeli attacks have killed 105 people since Sunday across the country.