The rockets were the latest in a spate of launches by militants in the devastated Palestinian territory, with Israeli Defence Minister Israel Katz warning this week of even more intense retaliatory strikes if they continued.
After more than 14 months of war between Israel and Palestinian Hamas militants in Gaza, such launches had become rare. They have intensified since late December as Israel continues a three-month major land and air offensive in the territory's north.
The military said one of Friday's rockets "fell adjacent to the community of Nir Am", in Israel off the northeastern tip of Gaza, while the second landed in an uninhabited area.
Earlier in the day, it said another rocket fired from Gaza had triggered sirens near Beeri, opposite central Gaza.
No injuries were reported.
In Gaza, first responders said they recovered the bodies of 16 Palestinians, several of them children.
The strikes occurred on Gaza City, the central Maghazi refugee camp and the southern city of Rafah, said Mahmud Bassal, spokesman for Gaza's Civil Defence.
"Friday was a harsh day for the residents of Gaza, particularly in Gaza City, due to the continuous Israeli bombardment," he told AFP.
Several of the fatalities occurred in strikes and shelling on northern and central Gaza, and two were in the south, he said.
Three children were killed in Israeli shelling in Gaza City's Zietun neighbourhood, while an air strike killed two people in the southern area of Rafah, Civil Defence said.
The Israeli military said in a statement that during the past day, "the Israeli air force struck approximately 40 Hamas terrorist gathering points" throughout Gaza.
Some of the targets "were embedded in areas that previously served as schools", it said.
- Hospital 'pile of rubble' -
Bassal denied the military's accusation, and alleged the military were "preventing food and drinking water from reaching dozens of medical staff, patients, and the injured" at the Indonesian Hospital in the town of Beit Lahia in the northern Gaza Strip.
He said his agency had received distress calls from the hospital since Thursday, adding that the facility is now "just a pile of rubble and walls. There's no hospital."
Late Friday, the military said it had not struck the Indonesian Hospital over the past day or damaged any essential equipment.
It added "there is no need to evacuate the hospital" and the military is coordinating with hospital officials to enable supply of humanitarian assistance to the facility.
On Sunday, a United Nations aid team visited the Indonesian Hospital.
"Around me there's nothing but rubble and destruction," said Jonathan Whittall, a UN aid official in a video released after he visited the hospital.
Israel's military has regularly accused Hamas of using hospitals as command centres, which the militants deny.
A report published Tuesday by the United Nations Human Rights Office said "insufficient information" has been made available to substantiate "vague" Israeli accusations of military use of hospitals.
The Israeli army has conducted intense raids in Gaza's north since October 6, saying it is an effort to prevent Hamas militants from regrouping there.
United Nations rights experts on Monday said the north Gaza "siege" appears to be part of an effort "to permanently displace the local population as a precursor to Gaza's annexation".
Bassal estimated that 10,000 people remained in the northern towns of Jabalia, Beit Lahia and Beit Hanoun, down from between 150,000 and 200,000 before the war.
Earlier this week, Katz warned that Israel would step up strikes in Gaza if the rocket fire did not stop and if hostages still held in the territory are not released.
The war in Gaza began with Hamas's October 7 attack on Israel last year, which resulted in the deaths of 1,208 people, mostly civilians, according to an AFP tally based on official Israeli figures.
Israel's retaliatory response has so far killed at least 45,658 people in Gaza, the majority civilians, according to the Hamas-run territory's health ministry, figures which the United Nations considers reliable.
The Israeli military on Friday also said it shot down a missile and a drone launched from Yemen, where Iran-backed rebels have stepped up attacks targeting Israel since a November ceasefire between Israel and another Iran-backed group, Hezbollah, in Lebanon.
Israel has also struck Yemen, including targeting Sanaa's international airport at the end of December.
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