But others argue that, while change is definitely in the air, the outreach is purely tactical and of limited intent on both sides. Vast differences remain, particularly over critical issues such as regime change in Syria and a big power-sponsored nuclear deal with Saudi Arabia’s archenemy, Iran.

“In the past, relations between Russia and Saudi Arabia were very bad, so any movement is going to attract notice,” says Irina Zvyagelskaya, a Middle East expert at the official Institute of Oriental Studies in Moscow. “But I wouldn’t exaggerate this. Everyone is jockeying for a better position, seeking what advantages they can, but there are no earthshaking changes underway here.”

Mr. Putin and Prince Salman sat down for a friendly meeting on the sidelines of a St. Peterburg economic forum last month, where they reportedly signed six deals, including a nuclear cooperation agreement that could see Russia helping to build up to 16 atomic power stations in the desert kingdom. They also are reported to have inked contracts on  space cooperation, infrastructure development, and a deal on high-end Russian weaponry.