Strikes come at a time of renewed tensions between Israel and Palestinian armed groups
Israel strikes Gaza targets after rockets fired from enclave
Israeli warplanes pounded the Gaza Strip early on Wednesday after two rockets from the Palestinian territory hit an Israeli city, in a blow to efforts to avert a new war.
Hamas disavowed the rocket fire saying they rejected "all irresponsible attempts" to undermine Egyptian efforts to broker a new long-term truce.
Israel Defence Minister Avigdor Lieberman ordered the closure of both border crossings with the enclave.
COGAT, the defence ministry body responsible for Palestinian civil affairs, said Mr Lieberman had ordered the closure of the Kerem Shalom goods crossing and the Erez crossing for people, as well as the reduction of the permitted fishing zone along the Gaza coast to three nautical miles.
The Israeli police said that "a rocket struck the city of Beersheba a few moments ago causing damage", although it did not specify the extent of the destruction. There were no reports of injuries.
The rocket fell into the garden of a house occupied by a family with three children who were being treated for shock, local media reported. The other came down in the sea off Tel Aviv, 70 kilometres from Gaza, the army said.
In retaliation Israel struck 20 targets in Gaza, killing one Palestinian, according to the Hamas-run health ministry.
It was unclear who fired the projectiles but the Israeli army says it holds Hamas accountable for what is happening in the territory under its control and commonly retaliates against them after such incidents.
It comes after months of violent Palestinian protests on the Gaza border, sparking deadly gunfire from Israeli troops and fears of an all-out conflict between Hamas and Israel, which have fought three wars since 2008.
At least 205 Palestinians and one Israeli have been killed since March 30.
Israel's defence minister said on Tuesday that the protests could not be allowed to go on.
"We are not prepared to accept the level of violence we see week after week," Mr Lieberman told troops and commanders at an army base near southern Israel's border with Hamas-ruled Gaza.
He also suspended shipments of fuel that had been trucked daily into Gaza over the previous week under a deal brokered by the UN and backed by the United States, Israel and others.
It had seen thousands of litres brought into the fuel-starved Gaza strip.
The UN says Israel's 11-year blockade of the enclave, ruled by Hamas, has resulted in a "catastrophic" humanitarian situation.
Gaza's two million residents endure dire living conditions including a shortage of safe drinking water and regular power cuts, partly due to a lack of fuel for the strip's power station.