The United States, the officials said, was caught by surprise: Egypt and the Emirates, both close allies and military partners, acted without informing Washington or seeking its consent, leaving the Obama administration on the sidelines. Egyptian officials explicitly denied the operation to American diplomats, the officials said.

The strikes are another high-risk and destabilizing salvo unleashed in a struggle for power that has broken out across the region in the aftermath of the Arab Spring revolts, pitting old-line Arab autocrats against Islamists.

Libya is the latest, and hottest, battleground. Several officials said that United States diplomats were fuming about the airstrikes, believing they could further inflame the Libyan conflict at a time when the United Nations and Western powers are seeking a peaceful resolution.

“We don’t see this as constructive at all,” said one senior American official.

Officials said that the government of Qatar has already provided weapons and support to the Islamist aligned forces inside Libya, so the new strikes represent a shift from proxy wars —where regional powers playout their agendas through local allies —to direct involvement.

The strikes have also proved counterproductive so-far: the Islamist militias fighting for control of Tripoli successfully seized its airport the night after they were hit with the second round of strikes.

American officials said Egypt had provided bases for the launch of the strikes. President Abdel-Fattah el-Sisi of Egypt and other officials have issued vigorous but carefully worded public statements denying any direct involvement inside Libya by Egyptian forces. In private, officials said, their denials had been more thorough.

The officials said that the U.A.E. — believed to have one of the most effective air forces in the region, thanks to American aid and training — provided the pilots, warplanes, and aerial refueling planes necessary for the fighters to bomb Tripoli out of bases in Egypt.

The U.A.E. has not commented directly on the strikes. But on Monday an Emirati state newspaper printed a statement from Anwar Gargash, minister of state for foreign affairs, calling questions about an Emirati role “an escape” from the recent election that he suggested showed a desire for “stability” and a rejection of the Islamists. The allegations about the U.A.E. role, he said, came from a group who “wanted to use the cloak of religion to achieve its political objectives,” and “the people discovered its lies and failures.”

The first strikes occurred before dawn a week ago, hitting positions in Tripoli controlled by Islamist-friendly militias, blowing up a small weapons depot, and killing six people.

A second set of airstrikes took place south of the city early on Saturday, hitting rocket launchers, military vehicles, and a warehouse all controlled by Islamist-allied militia.

The second strike might have been motivated by a desire to prevent animminent capture of the Tripoli airport by Islamist aligned militia, many of whom are based in the coastal city of Misurata and more tribal than Islamist in orientation. It had previously been held by militias based in Zintan and aligned against the Islamists. But after besieging the airport for a month, the Islamist aligned forces overtook it that night.

Responsibility for the airstrikes was initially a mystery. After the first set, several American officials initially said that signs pointed to the United Arab Emirates, but some said that the evidence was not conclusive.

Anti-Islamist forces based in eastern Libya under the renegade former general Khalifa Hifter sought to claim responsibility, but their statements were inconsistent and the strikes were beyond their known capabilities.

A former Qaddafi official now consulting with the Emirates, meanwhile, argued on the condition of anonymity that the strikes must be the work of the United States, contending that the Western powers had sought to deter the danger posed by Libya’s Islamists.

On Monday, however, American officials said that the second set of strikes had provided enough evidence to conclude that the Emirates were responsible, even provided the refueling ships necessary for fighters to reach Tripoli from Egypt.

The officials said this was not the first time that the Egyptians and Emirates had teamed up to strike against Islamist targets inside Libya. In recent months, a special forces team operating out of Egypt but possibly composed primarily of Emirates personnel had also successfully destroyed an Islamist camp in eastern Libya without detection.

American officials said the success of that earlier raid may have emboldened Egypt and the U.A.E. to think they could carry off the airstrikes without detection. Or the brazenness of the attack may reflect the vehemence of their determination to hold back or stamp out political Islam.