The source said a police patrol ordered them to stop and opened fire when they did not. The dead men were not carrying identification documents but were believed to be African.
Egyptian police have stepped up efforts in recent months to control the border with Israel, after an increase in human trafficking through Egypt. At least 19 migrants were killed by Egyptian border guards last year and seven this year.
The last such shooting was reported earlier this month.
The Sinai border is a main transit route for African migrants and refugees seeking work or asylum in Israel. Egyptian police say the smugglers who ferry migrants to the border region sometimes fire on security forces.
Egypt, which for years tolerated tens of thousands of African migrants on its territory, fears the unfettered flow of migrants at its Sinai border could pose a security threat in an area where Islamist militants sometimes find refuge.
Eritreans make up the largest single group of people trying to cross into Israel from Egypt, though Ethiopians and Sudanese also make the trek. Egypt has faced Israeli pressure to halt the flow.
Security sources said police also shot and injured one Eritrean and two Ethiopians making a separate attempt to cross into Israel on Saturday. The Eritrean and one of the Ethiopians were critically injured and sent to Al-Arish hospital for treatment.
