The first blast was close to an office belonging to the UN agency for Palestinian refugees UNRWA, although it is unclear whether that was the intended target.
A spokesman for Gaza’s Interior Ministry said that security forces were investigating the explosion of two devices in central Gaza City, which caused some damage to buildings but no injuries.
The explosions come a day after another explosive device went off near the Palestinian Cabinet headquarters in western Gaza City on late Friday.
The headquarters are located in the former home of President Mahmoud Abbas, having been moved there following the April 2014 reconciliation agreement between Hamas and the Palestinian Authority, intended to bring the parties together after nearly seven years of political division.
Gaza has seen a series of violent incidents in recent months, the majority involving attacks on the property of Fatah officials in the Hamas-dominated region.