"Three bodies, bearing gunshot wounds, were found on the road linking the [North Sinai] cities of Al-Arish and Sheikh Zuweid," the source, requesting anonymity, told The Anadolu Agency.
"The body of a boy, also bearing bullet wounds, was found on the road between Sheikh Zuweid and Rafah," the source said.
He added that the bodies had been taken to different hospitals, but stopped short of providing any details regarding the circumstances of their deaths.
No groups have claimed responsibility for the killings, while the Egyptian authorities have yet to comment on the assertions made by the security source.
On Monday, police found seven bodies in different parts of Egypt's restive North Sinai province.
Three other bodies were found on Saturday, two of which had reportedly been decapitated.
It is believed that militant groups operating in Sinai target those they suspect of collaborating with Egyptian or Israeli authorities.
The "Wilayat Sinai" group used to be known as "Ansar Beit al-Maqdis." But it changed its name last November after swearing allegiance to the Islamic State of Iraq and Levant, a militant group that managed to capture vast swathes of land in Iraq and Syria last summer.
Wilayat Sinai has claimed responsibility for numerous recent attacks on Egyptian army and police personnel in Sinai.
On Sunday, the group claimed responsibility for kidnapping an Egyptian police officer in Sinai.