Nickolay Mladenov, the UN's special coordinator for the Middle East peace process, said on Wednesday he was "deeply alarmed by the recent escalation of violence between Gaza and Israel, and particularly by today's mutiple rockets fired towards communities in southern Israel".
According to the IDF, the rockets were launched from the Hamas-run enclave and two were intercepted by the Iron Dome missile defence system.
Hamas's military wing said it was behind the rocket attacks.
It said the Palestinian "resistance" had fired a large number of projectiles at "enemy positions in the Gaza envelope".
Israeli Prime Minister Benjamin Netanyahu convened an emergency meeting of the security cabinet due to the growing tensions in the Gaza Strip which was attended by Defense Minister Avigdor Liberman and senior commanders.
At least 158 Palestinians have been killed in four months of weekly border protests and one Israeli soldier was shot dead by a Gaza sniper.
The Israel Defense Forces (IDF) said the violence broke out after militants shot at an IDF vehicle in Gaza on Wednesday.
A watchtower of the Qassam Brigades in Al Zaytun neighbourhood was targeted by the Israeli shelling.
Israel has not commented on the reported casualties in Gaza yet.
The exchange came amid continued attempts by Egypt to broker a broad cease-fire deal between Israel and Hamas.
A 34-year old man was lightly injured by broken glass, and damages to several cars were reported.
Parts of the town have been closed off and police bomb disposal units were at the scene of the strikes, a spokesman for the force said.
Israel has fought three wars with Palestinian militants in Gaza since 2008 and says the blockade is necessary to keep them from obtaining weapons or materials that could be used for military purposes.
The push for a long-term ceasefire agreement follows months of clashes between Israel and Hamas, marked by a surge in cross-border arson attacks, rocket fire, and violent clashes which brought the sides to the brink of a full-scale war in two separate military flare-ups in July. Twenty-four of the slain protesters were minors, the ministry has said.
Protesters demand the "right of return" to their homes and villages in historical Palestine, from which they were driven in 1948 to make way for the new state of Israel.
Israel halted the supply of petroleum and natural gas to Gaza last week in response to incendiary kites and balloons launched from Gaza into southern Israel.
United Nations officials have however called for the blockade to be lifted, citing deteriorating humanitarian conditions in the Palestinian enclave run by Islamist movement Hamas where 80 percent of the two million population are dependent on aid.