Western officials say Ansar Beit al-Maqdis includes cells of fighters scattered on both sides of the Nile. And they have capitalized on porous borders to obtain refuge and supplies from sympathetic militants to both the east and west of the country — in lawless eastern Libya on one side, and in the Palestinian territory of Gaza bordering Sinai on the other.

In Sinai, the suspicion that critical aid has flowed through the network of smuggling tunnels into Gaza is one reason that the Egyptian government took the drastic step of evacuating and destroying the homes of more than 1,100 families, all in a zone near the border.

In an audio statement on Monday pledging to “obey” Abu Bakr al-Baghdadi, the Islamic State’s leader and self-proclaimed caliph, Ansar Beit al-Maqdis also repeated a call to rise up against Egypt’s military-backed government — a trademark of its previous statements.

“To our people in Egypt, what are you waiting for after the violation of your dignity?” the statement asked. “After shedding the blood of your sons on the hands of this reckless tyrant and his soldiers? When will you take out your swords to face your enemies?”

It also added a familiar slap at the Muslim Brotherhood, the mainstream Islamist group that dominated Egypt’s free elections and backed the deposed president, Mohamed Morsi, only to end up crushed by the military takeover. “Shameful peace will do you no good, nor will blasphemous democracy,” the statement said, “and you have seen how it has claimed its upholders and their masters.”

Details about Ansar Beit al-Maqdis are scarce, in part because the Egyptian military limits access to the areas of Sinai that are the front line of its battle against the group. Its name means Supporters of Jerusalem, and Western officials estimate that it includes only hundreds or perhaps a few thousand fighters.

Western officials familiar with intelligence reports on the group’s internal communications say that a faction of Ansar Beit al-Maqdis based in the Nile Valley opposed the affiliation with the Islamic State. They worried that its reputation for careless violence will alienate other Egyptians, especially the disaffected Islamist youth that Ansar Beit al-Maqdis has sought to enlist.