Tensions have been rising along the northern border, with repeated scuffles between the IDF and Lebanese citizens.
The exercise is due to run for approximately two weeks, while the meeting with Kurilla took place on Tuesday at the Kirya in Tel Aviv.
One reason Israelis have been reluctant to embrace the one-state model is because of the debate over Israel’s future borders.
US President Joe Biden has pressed Israel to take steps to ease foreign travel for West Bank Palestinians since he entered office.
The incident was especially embarrassing because it was revealed publicly by Lebanese media after the man was back in Lebanon.
Approximately 4,000 people visited Ghajar the day the town opened to the rest of Israel. Another 6,000 visited the following day.