Agency spokesman Mahmud Bassal told AFP the first hit a tent housing displaced people in Khan Yunis in the south shortly after midnight local time (2100 GMT Tuesday) and the second struck a camp in the north soon afterwards.
The Israeli military said it was looking into the report when contacted by AFP.
The bombings came as Israeli Prime Minister Benjamin Netanyahu met US President Donald Trump in Washington and discussed the ongoing campaign to defeat Hamas in Gaza.
Afterwards, he restated Israel's aims to secure the release of all hostages taken during the Palestinian militants' October 7, 2023 attack, and "the elimination" of its "military and governing capabilities".
Gaza's civil defence agency said 29 people were killed in Israeli strikes across Gaza on Tuesday, with victims also including people displaced by 21 months of conflict.
Bassal said the first strike on Wednesday killed 10 members of the same family sheltering in the Al-Mawasi area of Khan Yunis while the second, on the Al-Shati camp near Gaza City, also left more than 30 wounded.
The victims were from two families, he added.
"The explosion was massive, like an earthquake," said Zuhair Judeh, 40, who saw the Al-Shati air strike.
"It destroyed the house and several nearby homes. The bodies and remains of the martyrs were scattered," he added, calling it "a horrific massacre".
Several people remained missing, presumed trapped under the rubble, he said.
Abeer al-Sharbasi, 36, described the air strike as "terrifying" and said it happened as she and her family were asleep in a nearby tent.
"You can't predict when or why they'll bomb you. We have nothing left but to surrender ourselves to God."
Due to restrictions imposed on media in the Gaza Strip and difficulties accessing the area, AFP is unable to independently verify the death tolls and details shared by the parties involved.
Hamas's October 7, 2023 attack on Israel resulted in the deaths of 1,219 people, mostly civilians, according to an AFP tally based on Israeli official figures.
Of 251 hostages seized during attack, 49 are still held in Gaza, including 27 the Israeli military says are dead.
Israel's retaliatory campaign has killed at least 57,575 people in Gaza, also mostly civilians, according to the Hamas-run territory's health ministry. The UN considers the figures reliable.
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