Israel's military says the two men were Hezbollah operatives, but the Iran-backed group accuses it of a ceasefire violation.
The US disputed Iran's claim the waterway is shut, a move Tehran says was a response to Israeli attacks in Lebanon.
The agreement followed concerns that continued clashes would undermine the deal to end the war between the US and Iran.
It comes a day after the US and Iran signed a deal to end their conflict, including fighting in Lebanon.
Many Lebanese remain doubtful that the agreement could finally mean the end of the fighting between Israel and Hezbollah.
Israel says it targeted the Iran-backed armed group Hezbollah, as Tehran warns this could derail a US-Iran deal to end the fighting.
Nine of them were killed in a series of attacks in the town of Tayr Debba, according to Lebanon's state news agency.
Iran warned Israel on Monday that it could resume hostilities if attacks on its Lebanese ally Hezbollah do not stop.
Israel's PM says his country is holding fire "at the moment", after Iran's armed forces said they had stopped military action.
