Hamas leader Ismail Haniyeh vowed to hold those responsible to account as Gaza's interior ministry declared a state of emergency.
He said the bombings would "not be able to undermine the stability and steadfastness of our people."
Hamas, which is considered a terrorist organisation by Israel, Britain and the US, recently released several prisoners from Salafist factions who have since challenged its rule of the Palestinian territory.
The releases had been described as a gesture of goodwill and include some members of militant groups affiliated with Isis.
One of the suspected bombers was one of the prisoners who had recently been released.
Israeli military sources denied launching any operations in Gaza.
