Before daybreak Wednesday, Israeli helicopters fired at gunmen in the southern city of Khan Younis, killing two, witnesses and hospital officials said.
The military said the target were gunmen who were approaching the border fence. Israeli forces began clearing the area near the fence, the military said.
Three Hamas members were killed Tuesday evening in two Israel Air Force strikes.
At first, the IAF struck a car in the southern Gaza Strip town of Rafah. One Hamas member who was in the car was killed, and another was critically wounded and later died of his wounds.
Palestinian sources said that the two were apparently on their way to fire rockets at Kibbutz Nahal Oz in southern Israel.
Sources in the Israel Defense Forces said that the two Hamas members were on their way to carry out a terror attack. According to the sources, after the car was hit there were sub-explosions, pointing to the fact that there were many weapons in the car.
Residents in the area reported of a loud explosion and fire bursting from the car, and of another two blasts immediately afterwards.
Shortly afterwards, the IAF struck another car, killing one Hamas member and injuring others.
Earlier Tuesday, IDF soldiers arrested a commander of Force 17, the Palestinian presidential guard in Ramallah, near Birzeit, in the Ramallah area.
The commander, Mahmoud Damra, also known as Abu Awad, is one of the most senior Palestinian security officers in the territories.
A senior Palestinian official, who is a close associate of Palestinian President Mahmoud Abbas, defined Damra's arrest as a "despicable act."
Hanan Greenberg and the AP contributed to the report