Hamas denied firing rockets at Israel on Tuesday afternoon in violation of a cease-fire that was supposed to have remained in place until midnight.
The IDF stated that three rockets were fired from the Strip despite the truce - two landing in the Beersheba area and one landing in Netivot.
The attacks, the first rocket strikes on Israel in some six days, prompted the IDF to respond with attacks on the Gaza Strip.
There was no immediate claim of responsibility for the attack, which the military said caused no casualties or damage. Sami Abu Zuhri, a spokesman for Hamas, said it had no knowledge of any rockets being fired.
Hamas accused Israel of escalating the situation in order to influence cease-fire negotiations in Cairo.
According to reports in Gaza, the IDF struck in Shejayia, in the Beit Lahiya area and in eastern Rafah. Two children were reported to have been moderately injured in the IAF strikes.
Prior to the firing of the rockets from Gaza toward Beersheba and Netivot, hundreds of Palestinian families vacated their homes in north and east Gaza and went to UNRWA facilities.
Hamas warned that if Prime Minister Binyamin Netanyahu "doesn't understand the message from the people of Gaza in diplomatic language in Cairo, we know the way that will force him to understand."
Hamas spokesman Husam Badran accused Israel of sabotaging the talks, saying that the Jewish state was placing obstacles on every issue. "If we don't reach an agreement that serves the interests of the Palestinians, all options are open."
Senior Hamas official Izzat a-Rishek, a member of the Palestinian delegation to Cairo, said that "our people's struggle will not stop with this truce or any other. The struggle will continue until we achieve the goals of the people and fulfill the dream of elections and national independence."
Reuters contributed to this report.