The fighter jets staged mock bombing raids over the southern port city of Sidon and Ain al-Hilwe, the largest Palestinian refugee camp in the country.
Hizb Allah ousted Israeli troops
from south Lebanon in 2000
Israeli aircrafts also swooped low over the southern town of Bint Jbeil.
“The air defence unit of the Islamic Resistance (Hizb Allah’s military wing) confronted… Israeli enemy warplanes that violated Lebanese sovereignty”, a statement issued by Hizb Allah said.
Hizb Allah forced Israel to pull out its troops from southern Lebanon in May 2000 after 22 years of occupation.
The Shiite party is backed by Syria and Iran.
Israeli jets often violate Lebanon’s airspace, sometimes flying as far north as Tripoli and break the sound barrier over towns and cities.
The United Nations called on Israel to stop its flights over Lebanon in February, saying they could lead to an escalation.
Washington has Hizb Allah on its lists of terrorist organisations and has exerted pressure on the Lebanese, Syrian and Iranian government to disarm the resistance group.
The United States wants to see Hizb Allah on the "terror" lists of its ally countries.
On Monday, the Australian parliament passed a bill, banning what it called Hizb Allah’s “external security” group, which Australian intelligence claims is linked to “terrorist” activities.
Hizb Allah says it has no external branches and that its activities are limited to Lebanon.
Attorney-General Daryl Williams said in a statement the ban would be backdated to 5 June once the group was officially listed.
Australia strengthened its counter-terrorism laws following the September 11 attacks in the US.
Anyone suspected of training, funding or recruiting members from a banned “terrorist” group could be imprisoned for up to 25 years.
The Australian Security Intelligence Organisation said there were Hizb Allah sympathisers and supporters in Australia, which has a large Lebanese community.
Last year, Canada outlawed Hizb Allah, while Britain has what it calls Hizb Allah's "External Security Organisation" on its list of "terorist" groups.