Lebanese and Israeli troops have exchanged fire along their border with each reporting casualties.
Lebanese officials say three soldiers and a journalist died under Israeli fire, after Israeli troops crossed the border on Tuesday.
Israel says two of its soldiers have been shot in a buffer zone, but troops remained on its side.
The incident is the most serious since a brief war between Israel and Hizbollah in 2006.
In a statement, Prime Minister Saad Hariri of Lebanon said Lebanese sovereignty had been violated.
The United Nations Security Council has met in an urgent session in New York to consider the incident.
On Monday, rockets were fired at the Israeli resort of Eilat, with a stray rocket killing one person in the nearby port of Aqaba in Jordan.