If finalized, the agreement would give Russia its deepest presence in Egypt since 1973, when Cairo expelled the military of the Soviet Union and instead became Washington’s closest Arab ally.

The United States has provided Egypt more than $70 billion in aid in the four decades since, at a rate of more than $1.3 billion a year in recent years. The cost is often justified in part by the argument that it secures the use of Egypt’s airspace and bases for the American military.

Egyptian and American analysts called the preliminary deal the latest sign of the waning influence of the United States as President Trump has diminished its military and diplomatic footprint in the region and the world.

“Power abhors a vacuum and when the United States pulls back we can’t be under the impression that the world is going to stand by and wait for us,” said Matthew Spence, a former deputy assistant secretary of defense for Middle East policy under the Obama administration, which faced similar criticism for its policy toward the region. “The danger, and the reality, is that other countries will take advantage of the opportunity presented when America chooses to pull back.”

In practical terms, the presence of Russian jets in Egypt would raise concerns about the operational security of American military personnel and require coordinating with American military planes in the same airspace.

“It’s a major problem for the United States-Egypt defense relationship,” said Andrew Miller, a former senior State Department official who is now at the Project on Middle East Democracy.

It was unclear to what extent Washington was informed about the agreement. The Trump administration has not yet replaced the ambassador to Cairo, whose three-year term ended in July.

Edgar Vasquez, a State Department spokesman, said only, “We are aware of these reports and are monitoring the situation.”

News of the preliminary agreement came as the United States diplomatic corps has been severely reduced and American foreign policy is facing challenges from all corners.

North Korea had tested its longest-range missile yet the day before, in defiance of bellicose warnings from Mr. Trump and at a time when the positions of assistant secretary of state for East Asia and American ambassador to South Korea both remain empty.

The prime minister and Parliament of Britain, Washington’s closest ally, have publicly rebuked Mr. Trump for promoting online videos from a British far-right group demonizing Muslims.

In the Middle East, the administration has no assistant secretary of state for Near Eastern affairs or ambassadors to Saudi Arabia, Turkey, Jordan, Egypt or Qatar. And on Thursday, a White House plan surfaced to oust Secretary of State Rex W. Tillerson, who had presided over the mass resignations of senior diplomats while watching his authority undermined by repeated contradiction or belittling from the Oval Office.

The Obama administration had been criticized by allies for retreating from the Middle East, in particular for failing to intervene aggressively enough against the Iranian- and Russian-backed government of President Bashar al-Assad of Syria in his civil war against rebels challenging his rule.

Under Mr. Trump, the United States has further reduced its support for Syrian rebelsbacked off its onetime goal of removing Mr. Assad from power and taken a back seat to Moscow in the Syrian peace process.

President Vladimir V. Putin of Russia has stepped in, expanding Moscow’s influence in the Middle East and seeking to regain influence lost with the collapse of the Soviet Union, the end of the Cold War and the expansion of America’s military presence around the Persian Gulf and elsewhere.

Russia has carried out an aggressive air campaign in Syria that has fortified Mr. Assad, cementing his position as a client of Moscow and protecting a Russian naval base on Syria’s Mediterranean coast.

Russia has sought to make inroads with American allies as well. In September, it agreed to sell $2 billion worth of advanced missiles to Turkey, a NATO member that previously clashed with Russia over its Syria policy. In October, Russia agreed to sell $3 billion worth of missiles to Saudi Arabia, another close American ally on the other side of the Syrian conflict.

With Washington seemingly in retreat, “very few if any of the states in the region are willing to rely solely on alliance with the United States and depend on the United States as the insurance policy for their security,” said Gamal Abdel Gawad Soltan, a scholar at the Al Ahram Center for Political and Strategic Studies, a state-financed research institute in Cairo.

In contrast, he said, “Russia has proven to be quite effective, and that has been attractive to countries around the region.”

Egypt, under the rule of Gamal Abdel Nasser, tried in the early 1950s to build counterbalancing alliances with the United States and the Soviet Union. But Washington soon lost patience with Nasser’s nonalignment policy and his anti-colonialist speeches, and Egypt fell more fully into the camp of the Soviets until the 1970s, when President Anwar Sadat switched his allegiance to the West.

Egypt’s current president, Abdel Fattah el-Sisi, who took power in a military takeover that ousted an Islamist president in 2013, has been rekindling Cairo’s Cold War alliance with Moscow. American officials believed he may have been trying to press Washington to keep delivering more aid of its own, a variation of Nasser’s strategy of playing off global rivals.

But American officials have scoffed at the idea that Russia could provide the kind of military support that the Soviet Union once promised, much less replace the supplies, training and maintenance that the Egyptians have come to depend on from Washington.

“Egypt would often hold out Russia as an alternative to American cooperation, and our attitude to some degree was, ‘Good luck with that!’ ” said Mr. Spence, the former Defense Department official.

But when the Obama administration temporarily suspended military aid to Egypt in 2013 in response to the government’s mass shootings of more than a thousand of his political opponents, Mr. Sisi visited Moscow and agreed to buy $3.5 billion in jets, helicopters and missiles from Russia. Last year, the two countries held joint antiterrorism drills, with Russian paratroopers conducting training exercises in Egypt with Egyptian paratroopers.

Egypt also signed a preliminary agreement for Russia to build nuclear power facilities in Egypt, although there has been no sign of any construction.

Mr. Sisi and Mr. Putin have collaborated more concretely to support a shared ally in Libya, Gen. Khalifa Hifter, who is based in eastern Libya across the border from Egypt. Russia has established a small military presence in a remote part of Egypt’s western desert to back the general, according to American officials briefed in the situation.

Their support for General Hifter has put Egypt and Russia at odds with the United States and other Western powers, which have backed a unity government in Tripoli in an attempt to end the civil strife that has plagued Libya.

It was not immediately clear what Egypt hoped to receive in return for allowing Russia to use its air bases or airspace. A draft agreement released by Moscow on Thursday gave Egypt only reciprocal rights to use Russian airspace or air bases, suggesting that Russia sought to obtain for free advantages for which the United States has being paying dearly for decades.

Some analysts speculated that Cairo might hope to persuade Moscow to restore tourist flights that it cut off because of security concerns after militants downed a Russian chartered jet leaving the resort of Sharm el Sheikh two years ago.

Egypt may also hope to persuade Russia to move ahead with the preliminary deal to build a nuclear power plant. “There is a long history of Russian preliminary agreements that take forever or never occur,” said Mr. Miller, the former State Department official.

Russian state media suggested that the agreement might help Moscow’s military campaign in Syria, another area where Mr. Putin and Mr. Sisi have found common ground.

Egypt’s Persian Gulf patrons, Saudi Arabia and the United Arab Emirates, have viewed the fight against the Assad government as a proxy war against its regional ally, Iran. But Mr. Sisi has sometimes shown sympathy for Mr. Assad as a fellow strongman defending the status quo and fighting political Islam.

Vladimir Fitin, head of the Near and Middle East Center at the Russian Institute for Strategic Studies, said that access to Egyptian airports would allow Russian military aircraft to refuel on their way to Syria, according to a report by RIA Novosti, a state-controlled Russian news service.