CAIRO — In just the last two weeks, Islamist militants have detonated a car bomb at the gates of the capital’s security headquarters, gunned down a senior Interior Ministry official in broad daylight and shot down a military helicopter over Sinai with a portable surface-to-air missile.

But perhaps most alarming to officials in Cairo and Washington are the signs that the swift increase in the scale and effectiveness of the attacks may come from a new influx of fighters: Egyptians returning from jihad abroad to join a campaign of terrorism against the military-backed government.

“Egypt is again an open front for jihad,” said Brian Fishman, a researcher in counterterrorism at the New America Foundation in Washington. “The world is being turned on its head, and, for the United States, the ability to rely on Egypt as a stabilizing force in the region — rather than a source of problems — is really being challenged.”

The birthplace of political Islam, Egypt has sent fighters to battle zones from Kandahar to the Caucasus for decades, and in the late 1990s its security forces crushed an Islamist insurgency at home. But until last summer, when the military ousted President Mohamed Morsi and began a bloody crackdown on his allies in the Muslim Brotherhood, Egypt remained largely insulated from the Islamist violence that flared up around it.

Now the new government is facing a new campaign of terrorism — set off by anger at Mr. Morsi’s ouster but also tied to the Islamist and sectarian violence engulfing the region.

The Arab Spring revolt that initially carried Islamists to power through democratic elections in Egypt also brought a sectarian civil war to Syria, helped reignite similar fighting in Iraq, led to the near-collapse of the Libyan state and the looting of its arms depots, and opened a broad zone of permeable borders across North Africa that jihadists can traffic with ease.

Then, after Mr. Morsi’s ouster in July, militants across the region turned their attention once again to Egypt. The military overthrow of a freely elected Islamist fulfilled the predictions of jihadist ideologies that power could never be won through democracy, and they have pounced on the opportunity to proclaim their vindication.

International terrorist groups like Al Qaeda and the Islamic State of Iraq and Syria, or ISIS, began calling for Muslims inside and outside of Egypt to take up arms against the government. Now a growing number of experienced Egyptian jihadists are heeding that call, often under the banner of Sinai-based militant groups such as Ansar Beit al-Maqdis, according to United States and Egyptian officials involved in counterterrorism. At least two Egyptians who returned from fighting in Syria have already killed themselves as suicide bombers, according to biographies released by the group.

Egyptian military officials say they have also captured Palestinians, Syrians and other foreigners among the terrorists in Sinai. But an American counterterrorism official said Washington believed Ansar Beit al-Maqdis “is largely Egyptian, including some who fought in other conflict zones before returning home,” along with “a relatively small contingent of battle-hardened foreigners.”

The jihadist homecoming appears to have provided the resources and expertise behind a quickening series of attacks that have far exceeded the abilities previously displayed in Egypt. Ansar Beit al-Maqdis has shown it can build and remotely detonate large bombs in strategic locations, gather intelligence about the precise timing of movements by their targets, record their own attacks and manage the complicated maintenance of an advanced portable surface-to-air missile — all suggesting combat experience.

“The number of attacks has gone up certainly over the past six weeks,” John O. Brennan, the director of the C.I.A., told a House hearing this week. “And some senior-level Egyptian officials have been killed at the hands of these terrorists.”

Egyptian military officials say they are determined to defeat this new wave of terrorists just as they defeated the insurgency that flared in the 1990s.

Back then, militants who insisted on armed struggle — including Ayman al-Zawahri, the Egyptian-born Al Qaeda leader — eventually gave up on the utility of armed struggle at home, refocusing on attacking Egypt’s Western sponsors.

But the ouster of Mr. Morsi appears to have changed that calculus.

“Zawahri and others have been saying from the beginning that they believed the military would come back, that the military and the West are not going to allow an Islamist government to stay in power,” said Aaron Zelin, a researcher at the Washington Institute for Near East Policy who tracks jihadist messages.

The Brotherhood, which has publicly denounced violence for decades, once helped combat militancy by channeling Islamist opposition into the political process. But the new government has now outlawed the Brotherhood.