The first blast struck at around midnight in eastern Gaza City outside the home of Nayef Khuweter, a Fatah official in the territory, police and eyewitnesses said.
Fatah condemned the attack, saying it would "disrupt" attempts at reconciliation with the Islamist movement Hamas which runs the Gaza Strip.
In a separate incident, a car exploded in Nuseirat refugee camp of central Gaza.
The Hamas-led police said they had opened investigations into the blasts, for which there were no immediate claims of responsibility.
Tension between the two rival parties has increased in recent weeks against the backdrop of an electricity crisis in Gaza and anti-Hamas protests.
Several reconciliation bids have failed, though the two were among several Palestinian parties which recommitted to forming a national unity government during talks in Russia on Tuesday.
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