A number of videos appear to show the Israeli Iron Dome missile defense system intercepting incoming missile from Gaza.
Israel and Egypt have maintained a blockade on Gaza since the Hamas takeover, a blockade that has devastated Gaza's economy.
Hamas called for an worldwide investigation into what it claimed was Israel's "deliberate targeting of civilians and civilian facilities", while the Israeli army claimed it has carried out a successful missile strike against the group's military intelligence headquarters.
Israeli Prime Minister Benjamin Netanyahu cut short a state visit to Paris commemorating the 100th anniversary of World War I returning to Israel. Israel said one of its soldiers had been killed in an exchange of fire before Israel called in tank fire and airstrikes while the commandos escaped back to Israel.
Since Monday, Israeli air strikes have killed seven Palestinians, at least five of them gunmen, armed factions said.
Hamas also fired a guided Kornet anti-tank missile at a moving IDF bus near Kfar Gaza shortly after 50 IDF soldiers had disembarked.
In Israel, at least 20 people have been wounded, several seriously.
Israel said it was an intelligence-gathering operation and that those efforts must continue to defend the country.
Hamas confirmed that the building in Gaza City was destroyed, while Islamic Jihad vowed to respond to Israel's action.
Israel's military said more than 80 rockets were launched from Gaza and it was conducting retaliatory air strikes for the fire it blamed on Hamas.
The escalation of violence has threatened to upend weeks of United Nations and Egyptian-led diplomacy to reach a long-term ceasefire between Israel and Hamas.
Lt. Gen. Gadi Eisenkot, chief of staff of the Israel Defense Forces, personally oversaw the covert mission along with the head of military intelligence, according to the Israeli newspaper Haaretz.
Israel is once again looking to instigate a war on Gaza. Twenty Israelis have been wounded in this bout of bloodshed. It also restricted movement through crossings with Israel, preventing foreign journalists, local businessmen and some aid workers from leaving the territory. The graphic footage shows a house in Ashkelon, on the Israeli Mediterranean coast, heavily struck by featuring the horrendous scene that the first responders to the attack witnessed upon entering the premises.
An Israeli aircraft fired towards a militant who was part of a group launching projectiles at its territory, the Israeli military said without confirming the death.
The botched Israeli raid in Gaza the day before left seven Palestinian militants and an Israeli officer dead.
"This is where Hamas' intelligence operatives gathered information to launch attacks on Israelis", the IDF said, adding that the group that controls Gaza "intentionally established their headquarters next to a school".
Since 2008, Israel has launched three major assaults on Gaza that have heavily damaged the Strip's infrastructure and sources of livelihood.
Before the flare-up, Netanyahu had defended his decision to allow Qatar to transfer the cash to Gaza despite criticism from within his own government over the move, saying he wanted to avoid a war if it was not necessary.
The agreements had led to calmer protests along the Gaza border after months of deadly unrest.