A large salvo of rockets fell onto the southern Israeli city of Ashkelon on Tuesday in what Hamas said was in response to deadly air raids on the Gaza Strip which have killed hundreds of civilians.
Shortly after, missiles were also fired from southern Lebanon into northern Israel, as the Israeli military responded by shelling border villages.
Hamas had warned Ashkelon's residents to flee hours before the attack on Tuesday. The flareup in southern Lebanon also came a day after several Hezbollah members were pronounced dead in Israeli air raids and artillery.
Israel kept up its deadly bombardment of the impoverished and heavily overcrowded Gaza Strip on Tuesday after Hamas threatened Monday night to execute some of the around 150 hostages it abducted in a weekend assault, if Israeli air strikes continue without warning.
The war - dubbed by Hamas "Operation Al-Aqsa Floods" - has seen the death toll rise in Israel to over 1000, with 830 confirmed dead in Gaza. Thousands on both sides are wounded, some critically.
Also on Tuesday, Israel warned that it would bomb aid convoys travelling from Egypt to Gaza after imposing a full siege on the coastal enclave, Israeli media reported.
Gaza's Rafah border crossing with Egypt - its only one that bypasses Israel - was hit by an Israeli air strike on Tuesday for the second time in 24 hours, AFP reported.
Witnesses said the strike hit the no-man's land between the Egyptian and Palestinian gates, damaging the hall on the Palestinian side.
The United Nations said Tuesday that Israel's siege on Gaza was "prohibited" under international law and called for the establishment of "a humanitarian corridor".
US President Joe Biden later said Hamas' attack was 'sheer evil' but failed to condemn Israel for its devastating bombardment of the Gaza strip that has killed hundreds, mostly civilians.
Rockets and shells were exchanged between Israel and militant groups in Lebanon and Syria, as tensions spread to countries neighbouring occupied Palestine.