Lebanon's government has been wedged into a war not of its choosing between Hezbollah and Israel, as the Iran-backed militants harden their stance and Israel demands the group's elimination.

Beirut has been struggling to pull the country back from the brink after Hezbollah drew Lebanon into the Middle East war on March 2, firing rockets into Israel to avenge the killing of Iran's supreme leader.

Khalil and his young family are sheltering in a theater in south Lebanon's Tyre, refusing to leave despite Israeli bombardment on the city that is now almost cut off from the rest of the country.

U.N. Secretary-General Antonio Guterres said Wednesday that fighting between Israel and Hezbollah must not condemn Lebanon to the same fate as Gaza, the Palestinian territory decimated by years of conflict.

Hezbollah chief Sheikh Naim Qassem said Wednesday that negotiating with Israel under fire would amount to "surrender" for Lebanon, and urged the government to reverse its ban on the party's military activities.

"When negotiations with the Israeli enemy are proposed under fire, this is an imposition of surrender," Qassem said, rejecting the Lebanese president's initiative to start direct negotiations "with an enemy that occupies our land and carries out daily attacks".

The Lebanese Army confirmed Wednesday that the projectile that exploded over Keserwan on Tuesday was an Iranian ballistic missile.

Israel launched strikes on south Lebanon and Beirut's southern suburbs on Wednesday, as Hezbollah said it kept up attacks on Israeli troops.

The Israeli military said on Tuesday that it was operating "according to an unchanged plan" in Iran and Lebanon, regardless of any talks aimed at reaching an agreement to end the hostilities.

Israeli emergency services said a woman was killed in the north of the country on Tuesday following rocket fire from Lebanon, where Israeli forces are fighting Iran-backed Hezbollah.

The Israeli military said a ballistic missile launched from Iran fell in Lebanese territory on Tuesday, as the Middle East war dragged into its fourth week.

"Following an assessment and based on the data available to the IDF (Israeli army), alongside the launches carried out toward the State of Israel earlier today, a ballistic missile fired by the Iranian terror regime fell in Beirut," a military statement said, referring to the missile fragments that landed in various areas of Keserwan and Metn earlier in the day.

Hezbollah on Tuesday called the decision by Lebanon's foreign ministry to expel the newly appointed Iranian ambassador a "sin", and demanded the authorities "immediately reverse" the move.