"It's time that Hamas decide to either fight or take care of its population. It's unacceptable that people in Sderot are living in fear every day and people in the Gaza Strip are living life as usual."
Israel kept all crossings into Gaza closed Friday morning, meaning that about 20 trucks of food scheduled to pass during the day would not be allowed through, Dror said.
The crossings are routinely closed on Saturdays, and may not be opened on Sunday morning if the rocket fire continues, he said.
The UN agency in charge of Palestinian refugees, UNRWA, condemned the Israeli move.
"This can only lead to the deterioration of an already dire situation," said Christopher Gunness, an UNRWA spokesman, said.
The closure "can only lead to the further radicalisation of a depressed and demoralised people".
At the same, Israel is pushing ahead with its military offensive against fighters in both Gaza and the West Bank.
The Israeli military has particularly intensified its operations in Gaza, with at least 32 people killed during the past week.
At least 19 people were killed on Tuesday alone.
In response, Hamas has begun firing rockets at Israel for the first time in months.
Some 150 rockets and mortars have struck since Tuesday, the Israeli army said.
In the latest operation, Israeli soldiers have killed a fighter from al-Aqsa Martyrs Brigades, an armed group loosely tied to Fatah, the party led by Mahmoud Abbas, the Palestinian president, medical officials and the group said.
Ahmad Sanakreh, 23, was a senior commander of the brigades.
The group confirmed that Sanakreh was killed on Friday morning by undercover Israeli troops operating in the Balata refugee camp near the city of Nablus.
Gaza air strike
Around the same time, an Israeli air strike killed a Palestinian fighter and wounded four other people in the north of the Gaza Strip, medics and witnesses said.
The raid happened near the town of Jabaliya, they said.
It was not immediately clear to which group the man belonged, they said.
An Israeli army spokeswoman confirmed an air strike in northern Gaza, aimed "at a rocket-launching squad after they launched rockets into Israel".
The latest offensive comes amid a statement by Ehud Olmert, the Israeli prime minister, that his country was at "war" against fighters in the Gaza Strip.
"A war is going on in the south, every day, every night," he said on Thursday.
"We cannot and will not tolerate this increasing fire at Israeli citizens ... so we will continue to operate, with wisdom and daring, with the maximum precision that will enable us to hit those who want to attack us."
Al Jazeera's Nour Odeh, reporting from Ramallah, said that residents of Gaza believe they are targeted no matter what they do, and that they are being subjected to indiscriminate attacks.
She said: "Even civilians are living in fear ... Bear in mind that Gaza has been closed from the rest of the world since June last year when Hamas took over Gaza.
"Now the Erez crossing - a small gateway in the northern Gaza Strip, through which aid supplies were delivered - is also closed.
"This is set to make conditions even worse for Gazans."