Over the past four months, 163 Palestinians have been killed by Israeli fire, including at least 120 protesters, according to the Gaza Health Ministry and a local rights group.
The strike hit a building that Palestinians say housed a cultural centre and other offices in the middle of the city, an AFP correspondent said.
Nickolay Mladenov, the United Nations special envoy who is involved in Egyptian efforts to broker a truce, said in a statement on Thursday that he's "deeply alarmed" by "multiple rockets fired toward communities in southern Israel" the day before.
Air raid sirens signaling incoming rocket fire wailed across southern Israel throughout Thursday, with warnings going off in the southern city of Beersheba for the first time since the 2014 war.
Gaza's militant Islamic Hamas rulers and Israel appeared to be honoring a cease-fire Friday that ended two days of an intense flare-up in violence amid efforts by neighboring Egypt to negotiate between the two sides.
Nearly 200 rockets and mortar shells were fired from within Gaza by Hamas and other Palestinian movements at towns and villages in Israel, provoking a similar number of attacks by the Israeli Air Force.
At least seven civilians were injured by the rocket fire on the Israeli side.
It said the Palestinian "resistance" had fired a large number of rockets at "enemy positions in the Gaza envelope".
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Just as they joined forces to eradicate these brushfires, Greenblatt said, Israelis and Palestinians must work together to "address another deadly threat: Hamas".
"The principle of returning [captured] soldiers, alive, wounded or dead - is a principle we all grew up on, and must not allow to be lost", he said.
"The government is in dire need of individual initiatives and investments to provide power so that it can become independent of the occupation (Israel), step by step", Shifa' Abu Sa'adi, head of natural resources at the Palestinian economy ministry, told Reuters.
Two Palestinian officials said on condition of anonymity that Gaza militants halted rocket fire at noon on Thursday.
"We urge the Palestinians and the Israelis to display restraint and to take measures towards ruling out the relapses of violence with unpredictable aftermaths", Zakharova said.
Rocket sirens were still sounding in Israeli neighborhoods on Wednesday evening, while strikes in Gaza continued.
The Hamas announcement came shortly after Israeli prime minister Benjamin Netanyahu's security cabinet ordered the army to take unspecified "strong action" against Gaza militants as the military reinforced units along the border.
Three Palestinians were killed during pre dawn Israeli airstrikes on the besieged Gaza Strip Thursday.
In a statement, Palestinian Authority President Mahmoud Abbas called for the global community to step in, blaming Israel for "the escalation on our people in the Gaza Strip". An Israeli soldier was killed by a Gaza sniper during this same period.
The situation around Gaza deteriorated sharply on Wednesday night when the radical Palestinian groups opened intensive shelling of the Israeli territory in response to the killing of two Palestinian fighters, who did not pose any risk to the Israelis.