Israeli officials argue that Lebanon is not covered by the ceasefire agreement.
The Israeli Defence Forces early on Tuesday said it was striking sites belonging to the Hezbollah militia in Beirut.
The originally planned withdrawal of Israeli troops from southern Lebanon within 60 days has been delayed.
For Tehran, al-Assad was a strategically important ally in its self-declared resistance front against arch-enemy Israel.
Mr Erdoğan separately called for an end to the fighting in the Gaza Strip.
Two people have been killed in northern Israel amid a barrage of some 60 rockets fired from Lebanon, the Israeli military reported on Wednesday.
According to the Israeli military, 10 of its soldiers have died in the violence on the northern border.
