"We can not stand idle when we see two million Palestinians in Gaza living in such bad conditions as they do now".
In addition, the fishing area will be reduced from six miles to three miles beginning Tuesday.
Israeli forces and settlers pulled out of Gaza in 2005 and the enclave is now ruled by the Islamist group Hamas.
The primary target of the IAF strikes Saturday was the Hamas battalion headquarters in Beit Lahia, in the north of the Strip, the army said.
The steps come as the United Nations and Egypt push for a ceasefire between Israel and Hamas in the Gaza Strip, and as Israel prepares to go to war - if necessary - to prevent Hamas and the Islamic Jihad from launching rockets and incendiary devices into southern Israel.
Hamas warned Israel of "dangerous consequences" for the new fresh restrictions, calling them "a crime against humanity".
Palestinian fighters in Gaza fired a barrage of 200 rockets and mortars into southern Israel over the weekend.
The Israeli non-governmental organisation Gisha, which promotes freedom of movement for Palestinians, said the "shutting down of Gaza's main lifeline is an abhorrent act of illegal collective punishment against the two million residents of Gaza, most of whom are children".
Citing the daily Hebrew-language newspaper Israel Hayom, IPT said Hamas is preparing to mount explosive material on unmanned aerial vehicles to target Israel communities deeper into the country.
After Hamas accepted an Egypt-mediated ceasefire late Saturday, the situation calmed down, but flaming kites and balloons continued to waft over into Israel, with the military signalling a new policy of striking back immediately.
There have been no Israeli fatalities during the so-called "Great March of Return" demonstrations but big tracts of Israeli land have been ravaged by fires set by blazing kites or helium balloons carrying burning rags floated over from Gaza.
The European Union also criticized the restrictions, saying it "expects Israel to reverse these decisions" which risked "further aggravating the already dire economic situation in Gaza". The Strip has been subject to a strict blockade for the past 11 years that Israel says is necessary to prevent terrorist groups from bringing weapons into the Strip.
Gaza's only other functioning border crossing, Rafah, is with Egypt.