Israel said its military operations in Lebanon would continue despite Donald Trump’s ceasefire announcement, with Israeli forces carrying out strikes and telling civilians in the south of the country to leave the areas they are targeting.

The office of the Israeli prime minister, Benjamin Netanyahu, said that Trump’s two-week pause “does not include Lebanon” amid reports of continued artillery and drone strikes, directly contradicting statements made by Iran and Pakistan, which has been mediating in the conflict.

Shehbaz Sharif, the prime minister of Pakistan, said that Iran, the US and their allies “have agreed to an immediate ceasefire everywhere including Lebanon and elsewhere” as he announced the ceasefire overnight.

Israel said it supported Trump’s decision to suspend strikes against Iran for two weeks provided Tehran opened the strait of Hormuz and stopped attacks on all countries in the region – but had emphasised for days that it considered Lebanon to be a separate conflict.

On Wednesday morning, a spokesperson for the Israeli military said it was “continuing its operations” against Hezbollah and told people in southern Lebanon to move north of the Zahrani River.

According to leaks, Iran’s 10-point peace plan, nominally accepted as a basis for negotiations by Trump, calls for an end of the war against “all components of the ‘axis of resistance’,” which, for Tehran, includes the pro-Iranian Lebanese group Hezbollah.

Trump did not refer to Lebanon in his ceasefire statements, which focused on Iran, leaving it unsettled whether Israel’s attacks on Lebanon, which have killed more than 1,500 people, many of them civilians, would come to a halt.

On Sunday night, Netanyahu told a meeting of Israel’s security cabinet that there would be no situation in which a ceasefire with Iran would be carried over into Lebanon. Political and military leaders agreed the war should continue.

An hour before the Iran ceasefire was announced, Israel bombed a car in front of a row of beach-side cafes in Saida, killing eight people and wounding 22, according to the Lebanese ministry of health.

Israel continued striking Lebanon into the morning, hitting the south with artillery fire and carrying out two separate drone strikes on the town of Qana and al-Qleileh. Hezbollah said it had not responded overnight.

Israel’s military also issued a warning in Arabic to people in Tyre shortly after 9am to move away from a building, statements that typically come before an airstrike in a populated area.

Lebanese sources told Reuters that Hezbollah is expected to issue a statement outlining its formal position on the ceasefire and on Netanyahu’s assertion that Lebanon is not included in the agreement.

Highways leading south were choked with traffic as dawn broke. Residents were attempting to return to their homes, though Hezbollah urged people not to return to certain villages because Israeli troops remained there.

WhatsApp chats were filled with anxious and hopeful messages between people in Lebanon as they tried to parse whether or not the country would be included in the Iran ceasefire.

The almost five weeks of war in Lebanon has brought the country to its breaking point, with more than 1.1 million people forcibly displaced, many of whom are living on the streets.

Several air raids on Israel took place in the first part of the night but stopped shortly before 3.30am, about 40 minutes after the Pakistani prime minister’s announcement. No incoming attacks have been reported since.