Among the issues he also raised was his concern over a number of incidents along the Israeli-Lebanese border in which the IDF fired on the United Nations peacekeepers.
The decision would be implemented in an attempt to prepare for an Iranian response to an Israel strike.
Since the beginning of the war, the Americans have been communicating mostly through Gallant as their primary channel instead of dealing directly with Netanyahu.
Israel faces a dilemma: How much of their plans should they share with the US?
Netanyahu and Biden are now expected to speak on Wednesday.
Austin was slated to travel to Israel late last month though his trip was cancelled due to escalating tensions with Lebanon.
Multiple times, the US has urged Israel to act less aggressively or not to take certain actions against Hezbollah, to avoid a larger regional war.
"Nasrallah's death from an Israeli airstrike is a measure of justice for his many victims, including thousands of Americans, Israelis, and Lebanese civilians," Biden said.
The Pentagon said it is assessing the event, but had no additional information or specifics to provide at this time.
There are thousands of American citizens in Lebanon, and a further escalation of the situation towards an all-out war could lead to an American decision to evacuate.