One terrorist was killed while another was critically wounded and taken to the hospital for treatment. A third was apprehended by the troops and taken in for questioning, while the fourth was apparently able to escape back into the strip.
The terrorists were trying to set fire to a sniper position on the border near Rafah in the southern part of the strip, which they also tried to set ablaze on Sunday.
"The terrorists crossed the border fence into Israeli territory equipped with cutters and flammable materials and tried to set fire to a vacant sniper position," the IDF said in a statement. "An IDF force identified the infiltration and monitored the incident. The force then opened fire in pursuit of the terrorists."
The army went on to say that "During the incident, the IDF force reported hearing gunfire in its direction. The force acted quickly against the violation of Israeli sovereignty and the attempt to sabotage security infrastructure."
"Hamas is responsible for everything that happens in the strip and anything that comes out of the strip and is behind the attempts to cross the fence and sabotage security infrastructure. The IDF views such incidents gravely and will continue operating against them in a decisive manner," the IDF statement concluded.
Gaza's health ministry said a 16-year-old Palestinian was wounded by Israeli gunfire in the southern Gaza Strip. It's unclear if the two incidents are related.
At the same time, the Knesset held a discussion ahead of a no-confidence vote over the "lack of government policy and strategy regarding the Gaza Strip."
According to an update given by Minister Gila Gamliel, some 450 incendiary kites were shot down by IDF drones; 260 Palestinians crossed the border fence and caused 203 fires; and some 19,000 dunams (some 47,000 acres) were destroyed as a result of the blazes in the Gaza border area, causing significant damage.
Also Monday afternoon, a large blaze was raging in the Shikma Stream area in the northern Negev. Some 200 dunams (about 50 acres) have been burned so far. Firefighting forces have yet to gain control of the fire.
Some 2,000 Palestinians gathered Friday afternoon in six places along the Gaza Strip border to protest, and hundreds of them approached the border fence. IDF forces responded with crowd-dispersal means. A 13-year-old boy and a 24-year-old man were killed in the clashes.
On Thursday afternoon, Palestinian sources reported that a 17-year-old Palestinian was killed by an IDF tank shell while approaching the border fence in the Gaza Strip overnight.
The tank fired at the teen after spotting two terrorists crawling towards the border fence in an attempt to infiltrate Israel from the southern strip.
The IDF said the tank had fired at the terrorists and thwarted the infiltration attempt. Molotov cocktails were found in the area.
The Associated Press contributed to this report.