The Israeli airstrikes were preceded last week by a wave of attacks against the military group, including the detonation of explosives in pagers and handheld radios that killed at least 37 people and injured thousands and a strike in Beirut against a top Hezbollah commander that left him and 50 others dead.

Across Lebanon, streets and highways were clogged with traffic as people fled the attacks, which many people fear will continue to widen. Authorities ordered schools closed and the buildings converted into shelters.

Many people are trying to make their way to Beirut, and others, fearing eventual strikes on the capital, are fleeing to mountains in the north. In the southern Lebanese area of Nabatieh, Lebanese state media reported an “unprecedented movement of ambulances” transporting dozens of injured people.

“Five missiles hit our house,” said Yasmine Mrouh. She had fled from the outskirts of the southern city of Saida to the Beirut area with her husband and their two daughters and was trying to find a room at a displacement shelter housed in the Hotel Technical School in a suburb called Dekwaneh. She said they had already been forced to flee once before, leaving their home in the border village of Ayta Chaab after hostilities broke out last year.

Ayat Nazzal, a Beirut resident with roots in southern Lebanon, said her brother’s house close to the city of Tyre was also hit by an Israeli strike. He and his family escaped but were stuck in traffic for hours trying to flee to Beirut.

The mayor of Aitroun, a small village close to the border with Israel, said the bombing sounded relentless. “People are definitely leaving. Do you want them to stay and die?” Salim Murad asked in frustration.

Israel also struck in the far north of the country, near the border with Syria. Lebanon’s Health Ministry said at least one person was killed and six injured in those strikes.

For its part, Hezbollah fired about 240 projectiles into Israel on Monday, according to the Israeli military, a day after the group carried out one of its deepest attacks since hostilities escalated in October, targeting an air base in northern Israel located 50km from the border.

In response to the escalating conflict, the United States will send a “small number” of additional personnel to the region to augment existing forces, Pentagon spokesman Major General Patrick Ryder told reporters on Monday. He declined to specify their exact number or mission.

David Wood, a senior analyst for the International Crisis Group focused on Lebanon, said the willingness of both sides in recent days to cause civilian casualties represented a “very worrying shift”. He pointed in particular at Israel.

“Until now, there had been a real effort to minimise civilian casualties because that is what is likely to trigger a massive operation,” Wood said. “But it seems like that thinking might have shifted for Israel.” He said although the expansion of fighting along the northern border was “not new, the rate of the expansion is really alarming,” adding that if the intensity of strikes continued, then they could constitute a “full-scale war.”

Leaders of both Israel and Hezbollah have signalled the nature of the conflict has shifted.

“I promised we would change the balance of power in the north – that is exactly what we are doing,” Netanyahu said. “We are destroying thousands of missiles and rockets aimed at the cities of Israel and its citizens.”

Hezbollah’s deputy leader Naim Qassem said on Sunday that the group had entered a “new phase” in its conflict with Israel. Speaking at the funeral of Ibrahim Aqil, a top Hezbollah commander killed in an Israeli airstrike on Friday, he promised an “open-ended battle of reckoning.”

The Lebanese Government directed hospitals in much of the country to cancel all elective surgeries to ensure capacity to treat casualties. Firas Abiad, Lebanon’s health minister, said Israel’s attacks over the past week had raised the number of wounded across Lebanon to 5000.

In Saida, in southern Lebanon, hospitals are receiving wounded with shrapnel injuries all over their bodies and severe burns, according to a doctor working there. The injured, including a large number of women and children, are mostly from nearby areas and said they were wounded when airstrikes hit their homes, the doctor said.

Israeli military spokesman Daniel Hagari said Lebanese civilians in the south and east of Lebanon, where strikes were concentrated, were told to evacuate from areas where Hezbollah stores and deploys weapons. The Israel Defence Force said in particular that warnings had been issued to civilians in the Bekaa Valley, where Hezbollah has a major presence, to “immediately distance yourselves” from such sites.

Some security experts questioned the effectiveness of those orders, which were delivered shortly before the strikes began, saying that evacuation warnings were also sent in parts of Lebanon that were not attacked, leaving residents around the country uncertain how seriously to take the orders. Lebanese officials, describing the warnings as part of Israel’s “psychological warfare,” said they caused confusion and panic.

Lama Fakih, Middle East and North Africa director for Human Rights Watch, said it is not the responsibility of civilians to “know where military objectives are”. Combatants on both sides have an obligation not to “co-locate” military assets in civilian areas and also to ensure “the risks to the civilian population from an attack should not outweigh the anticipated military advantage”.

Fakih said evacuation orders such as those issued by Israel are “not genuine warnings, but are primarily intended to cause panic or to displace people are prohibited”. She added that such fake warnings also “make people less likely to comply with true warnings.”

Imad Kreidieh, the chair of Ogero, which operates Lebanon’s telecommunications infrastructure, said that the country received more than 80,000 calls generated by the Israeli military. Lebanon’s information minister, Ziad Makary, said those calls urged residents to evacuate – which he described as “psychological warfare” – and he called on the public not to give “the matter more attention than it deserves”.

While Hezbollah rockets are able to strike as far south as Tel Aviv, Orna Mizrahi, a senior researcher at the Institute for National Security Studies, said the group so far appears cautious, limiting its attacks to areas farther north near the city of Haifa and the northwestern West Bank. She said that it seems Hezbollah wants to avoid further retaliation from Israel.

“We are just in the beginning of something new,” Mizrahi said, adding, “But we have a lot of plans and a range of options.”