"No terror element responsible for causing damage in Israel -- or to Israelis -- will be spared," he said on a tour of the area around Gaza, hours after two Thai workers were severely wounded and four others were lightly hurt by the rockets.
"If they cannot be calmed, and the rockets continue, then the IDF (military) will act," said Barak, noting that since the start of 2012, nearly 600 rockets and mortars had been fired at southern Israel.
"The issue is far from over. The struggle has not come to an end and it will not come to an end here in the next week."
Several hours after the militants fired the first rockets late Tuesday, Israeli aircraft killed two militants from Hamas' armed wing, the Ezzedine al-Qassam Brigades, in northern Gaza, sparking even more rocket fire.
An early-morning raid near southern city of Rafah killed a third militant from the Popular Resistance Committees (PRC), and later a Hamas militant hurt in the evening strikes died of his injuries, medics said.
Israel's military said armed groups had fired 72 rockets and mortar shells over the border since midnight, injuring six, two of them seriously. Police said two Thais were "seriously to critically wounded" and a third had light injuries.
Militants from Hamas and the PRC claimed responsibility for the rocket fire.
Later, the Hamas government issued a statement "condemning the Zionist aggression against the Gaza Strip," and warning of its consequences.
It called for Arab leaders to visit the Gaza Strip in solidarity with its people, while expressing "satisfaction of the historic visit of the emir of Qatar."
Palestinian negotiator Saeb Erakat said Israel "bears full responsibility for what happens to our people in Gaza," while UN peace envoy Robert Serry deplored the escalation and called on all parties to exercise utmost restraint.
The only crossing between Gaza and Israel in the north of the Palestinian territory was blocked, meanwhile, preventing dozens of people from travelling, including patients, said officials.
Israeli Prime Minister Benjamin Netanyahu warned any continuation of rocket fire would prompt a "much more extensive" Israeli response.
"We neither chose nor initiated this escalation but if it continues we are prepared for much more extensive and deeper action," Netanyahu said on a tour of the Iron Dome anti-missile battery near Ashkelon, which brought down eight rockets during the day.
"In any case, we will continue with preventative operations. Whoever intends to attack Israeli citizens needs to know that he will bear the consequences."
Netanyahu also said he had decided to increase protection for Israeli communities located 4.5-7 kilometres (2.8-4.3 miles) from the Gaza border, which were not covered by Iron Dome.
Chief of Staff Lieutenant General Benny Gantz also toured the south, an army statement said, indicating he "held an operational assessment looking at a continued military response in light of the escalation in the south."
Speaking to public radio, deputy foreign minister Danny Ayalon said Israel "must strengthen its deterrence against Hamas by attacking the heads of this terrorist organisation or by destabilising its rule."
But army spokesman Brigadier General Yoav Mordechai said overthrowing Hamas "would require a prolonged operation with multiple implications, mainly political.
"This option does exist but I don't think that we have reached the stage where we are talking about this option," he told the radio.
Tensions have been high around Gaza for the past few weeks, but peaked early on Tuesday when an Israeli soldier was severely injured by a roadside bomb in an attack claimed by the armed wing of the leftist Popular Front for the Liberation of Palestine.