A Hamas spokesman told Al Jazeera that Israel should be pressured by other countries to put an end to the raids.
“We know that the Gaza Strip is a small area. It is open for Israel – they can kill most of the Palestinian people and destroy everything,” Ghazi Hamad said.
“The job of the international community is to stop the Israeli crimes in the Gaza Strip.”
Barak’s threat of a full-scale invasion came as the Israeli military pounded Gaza on Thursday, killing 20 Palestinians, including five children playing football.
Khalil Ali, a commander in the armed wing of the Palestinian Popular Resistance Commitees, was among those killed on Thursday evening.
The Saftawi neighbourhood headquarters of the General Association of Palestian Workers was also hit.
Hamas, which has de facto control of Gaza, says it hit Israel with more than 80 rockets in the same period.
Israel’s deputy defence minister said that if Palestinian fighters were to use weapons with a longer range they would risk bringing a “shoah” – the Hebrew word for holocaust – upon the Palestinian people.
“The more Qassam fire intensifies and the rockets reach a longer range, they [the Palestinians] will bring upon themselves a bigger shoah because we will use all our might to defend ourselves,” Matan Vilnai told Army Radio on Friday.
However, Arye Mekel, Israel’s foreign ministry spokesman, said that Vilnai used the term “in the sense of a disaster or a catastrophe, and not in the sense of a holocaust.”
Sami Abu Zuhri, a Hamas official, strongly criticised Vilnai’s comments.
“We are facing new Nazis who want to kill and burn the Palestinian people,” he said.
Officials from Hamas struck a defiant tone on Thursday.
“We will never have equipment comparable to our enemy, but we are working all the time to have enough to make any aggression a regrettable adventure for the enemy,” Abu Obeida, a spokesman for Izz al-Din al-Qassam Brigades, Hamas’ military wing, said.
Along with its usual Qassam rockets that have a short range, Gaza fighters fired Iranian-made Grad rockets at Ashkelon, 17km north of Gaza.
One hit an apartment building, slicing through three floors and another landed near a school, wounding a 17-year-old girl.
The latest round of rocket fire was the most intense so far, and Uri Bar-Lev, the police chief, said it was the first time a building in Ashkelon was hit.
That pushed Ashkelon residents to demand better protection and Barak pledged to install a warning system within hours, defence officials said.
In Tokyo on Thursday, Condoleeza Rice, the US secretary of state, briefly met Ehud Olmert, the Israeli prime minister, and said the Hamas rocket attacks “need to stop”.
She also expressed concern for the humanitarian situation in Gaza, which is suffering shortages of certain basic goods due to a blockade imposed by Israel, and urged calm on all sides.
Rice is expected to visit the Middle East next week to help push peace efforts forward.
Nabil Abu Rdainah, a spokesman for Mahmoud Abbas, the Palestinian president, who is negotiating with Israel, said in a statement its military actions “meant only one thing: the Israeli government … aims to destroy the peace process”.
Olmert said at the end of a four-day visit to Japan that “the continuous shooting of Qassam rockets against uninvolved, innocent civilians is a major threat to the stability” of Israel‘s political contacts with Abbas’s Palestinian Authority.
He said, however, that he planned to hold another of his regular meetings with Abbas within the next two weeks.