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.