Workers had evacuated the building after the warning shots, and there were no immediate reports of casualties.
"Tonight, the IDF made sure that this station won't broadcast again", the army said.
The IDF said that Al-Aqsa TV was "used by [Hamas] for military activities, including sending messages to terrorist operatives in the West Bank, calls for terror attacks and instructions on how to commit them".
Lt. -Col. Jonathan Conricus, an Israeli military spokesperson, said Hamas and the Islamic Jihad group have more than 20,000 rockets and mortars, some capable of reaching Israel's main cities of Tel Aviv and Jerusalem. Israel said one military officer was killed and another was wounded in that fighting.
In the most serious strike, a mortar shell struck an Israeli bus, critically wounding a 19-year-old man.
It was the first confirmed death caused by the barrage of rocket fire from Gaza since Monday afternoon in a flare-up following a deadly Israeli special forces operation in the enclave. Some commenters suggested that the Israeli officials realized that such thinly-veiled threats to Palestinian civilians are not meant for the English-speaking audiences and erased it. Others suggested Twitter could have deleted it following complaints about threats of violence by other users. According to Israeli ambulance service, at least 7 people were injured during the attack.
Israel and Hamas have gone to war three times, and rocket-fire from Gaza and Israeli air strikes against militant targets are a regular occurrence.
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Palestinians said they discovered an undercover Israeli unit in a civilian auto about 3km (2 miles) inside the Gaza Strip late on Sunday.
Israeli Prime Minister Benjamin Netanyahu cut short a state visit to Paris commemorating the 100th anniversary of World War I returning to Israel. "The special operation yesterday was not meant to kill or abduct terrorists, but to strengthen Israeli security", a spokesperson said, adding that the battle was "very complex".
He added that the missiles' ability to overwhelm Israel's missile defences and hit houses will be "a awful blow" to Israel, adding that this was "the most serious escalation in fighting between Israel and Hamas since 2014 and in terms of the number of Israelis injured by missiles".
Israel had stressed its covert operation was an intelligence-gathering mission and "not an assassination or abduction", but Hamas strongly denounced it and vowed revenge.
A pursuit ensued and witnesses said Israeli aircraft fired more than 40 missiles into the area.
An exchange of fire followed in which local Al-Qassam commander Nour Baraka was killed along with another militant, it said.
The military provided few details about the reason for Sunday's raid.
For over seven months, Hamas has been leading protests along the Israeli border aimed in large part at breaking the blockade.
On Friday, Palestinian civil servants began receiving payments after months of sporadic salary disbursements in cash-strapped Gaza, with US$15 million delivered into the enclave through Israel in suitcases by Qatar. Seventy-three people, majority soldiers, were killed on the Israeli side.