The anniversary has been celebrated as a seminal modern moment for Jews, their return to rule over a united Jerusalem for the first time in about 2,000 years. But in recent years, the day itself has become favored more by the religious right. On Wednesday, as they do each year, young nationalist Jews paraded through the Arab Quarter singing and waving flags in front of stone-faced Palestinians, most of whom closed their shops in protest and fear.

“There is no wall,” said Sam Samir, 58, the Palestinian owner of a T-shirt shop, denying the Jews’ belief that their sacred temple once stood atop that site. Instead, Muslims revere the place as the home of Al Aqsa Mosque and the Dome of the Rock.

Even President Trump split the difference on the issues surrounding the Western Wall: It was among his first stops on his trip here this week, and he became the first sitting United States president to visit it. But he did so without Israeli officials and sidestepped the diplomatic issues around it.

The United States and most other nations have not recognized Israel’s annexation of territory captured in 1967, and both Israelis and Palestinians claim Jerusalem as their capital. The United States, like others, is waiting for a final deal between the two sides, which Mr. Trump says he is determined to broker.