The U.N. Interim Force in Lebanon last week said it took "very serious note" of an incident along the so-called Blue Line, an observed point of Israeli withdrawal from Lebanese territory in 1978.
Four Israeli soldiers were injured by an explosive device. The incident last week occurred a few hundred feet inside Lebanese territory near a UNIFIL observation post.
The peacekeeping force said last week it was investigating the incident. It said Friday it was clear the presence of Israeli troops inside Lebanese territory was a "serious breach" of U.N. Security Council resolutions.
Suleiman met Tuesday with caretaker Foreign Minister Adnan Mansour to discuss the incident.
A statement from the president's office, published by The Daily Star, said he condemned the incident and "asked Mansour to follow up on the matter with the Security Council."
Israeli officials last week said they were investigating whether the device was a remnant or something placed along the border recently.
UNIFIL said it "strongly protested" the border violation and called on the Israelis to cooperate fully with its investigation.