"My opinion on this matter is clear; every attack must be met with a response," Livni told Jerusalem Radio after a Grad rocket was fired at Asheklon, The Jerusalem Post reported.
The three-week Operation Cast Lead ended two weeks ago with Israel and Hamas -- which controls Gaza -- both declaring cease-fires.
Livni also rejected diplomatic overtures with Hamas, saying "any negotiations with Hamas, whether direct or indirect, are harmful. From a strategic standpoint ... I think that we should make peace with the moderate elements."
Following the rocket attack in Ashkelon, the Israeli military warned Rafah residents to leave their homes in case there was an airstrike.
The recorded messages, in Arabic, said people who work in tunnels, live near them or are "giving logistical help to terrorists" should evacuate the area immediately, residents told the Post.
Mark Regiv, a prime minister's office spokesman, said consequences would be grave if the rocket fire continued.
"Hamas is playing with fire and they alone will be responsible for the destruction of the truce," Regev said.