Hamas spokesman Fawzi Barhoum said the group was responsible for Saturday's barrage against Israel and that it was carried out "in response to the Israeli air strikes".
The Israeli military says it has struck several militant sites in Gaza in response to renewed violence along the border.
Israel's armed forces said dozens of strikes targeted military facilities belonging to the Gaza Strip's Islamist rulers Hamas, against which it has fought three wars over the past decade. The Iron Dome anti-missile defense system intercepted and shot down at least 30 of the missiles.
In Israel, air raid sirens sent people rushing to shelters in areas surrounding the Gaza Strip as rockets and mortars were fired from the Palestinian enclave at nearby communities.
In statements posted on Twitter, it said it struck two Hamas tunnels, one in southern Gaza and one in the north, as well as other infrastructure across the besieged coastal territory.
On Monday, Israel announced it was shutting down the Kerem Shalom border crossing - the Strip's main crossing for commercial goods - in response to the endless stream of incendiary and explosive kites and balloons that have been flown into southern Israel, sparking fires that have burned thousands of acres of land and caused millions of shekels in damages.
The two Palestinians killed were aged 15 and 16, caught in an Israeli strike on a building they were near in the west of Gaza City, the enclave's health ministry said.
"In consultation with the minister of defence, the chief of staff and the top security command of the state of Israel, we have decided on strong action against Hamas terrorism", Mr Netanyahu said in a video statement.
Israel says its use of live fire is necessary to defend its borders and stop infiltrations.
The blasts shook homes and shattered windows, and black plumes of smoke rose from the sites of the explosions.
Around 10 other passers-by were wounded, the officials said.
Israel says Hamas has been orchestrating the weekly protests to distract from governance problems and provide cover for militants' cross-border attacks.
"Troops responded by firing towards the terrorists", the military said. A police spokesman said no hits had been identified in the city.
Local residents were warned in advance of the IDF air strike, according to the IDF Spokesperson.
It said it fired toward a Palestinian who was attempting to infiltrate Israeli territory, but the incident appeared to be unrelated to the death of the teenager.
Hamas stopped short of claiming responsibility for the rocket fire, but Barhoum earlier called it "an immediate response by the resistance to the escalation" by Israel and a deterrence to further Israeli attacks.
There have been no Israeli fatalities during the so-called "Great March of Return" demonstrations.