The pro-Hezbollah newspaper Al-Akhbar described Abdullah's killing as “a harsh blow” to the group.
The paper said his killing “reflects a dangerous escalation on the part of the enemy” and “raises hopes that the confrontation will be managed differently.”
On Tuesday, Hezbollah said it fired about 50 rockets at Israeli targets in the occupied Golan Heights.
More than eight months of cross-border violence has killed at least 468 people in Lebanon, most of them fighters but also 89 civilians, according to an AFP tally.
Israeli officials say at least 15 Israeli soldiers and 11 civilians have been killed.
Thousands of people have been displaced on both sides of the border since violence flared a day after a Hamas attack on southern Israel.
The October 7 attacks killed 1,194 people in Israel, mostly civilians, according to an AFP count based on official Israeli figures.
Israel's counter-offensive against Hamas has killed at least 37,164 people in Gaza, the vast majority of them civilians, according to the Hamas-run territory's health ministry.