Even last week, the river was barely fordable, and Mr. Stevens and his escort had to go gingerly from one steppingstone to another, most half submerged, praying that delicate equipment evaded the drink.

His first impression, he said, was one of relief that, to the naked eye, the minaret did not appear to have moved significantly. Climbing its helical staircases is still possible — the steps remain intact, although entry is by ladder through an upstairs window, since the doors are now underground.

But after carrying out more precise measurements over the following days with sensitive instruments, Mr. Stevens came away concerned. While the minaret had only moved 16 to 28 millimeters since 2006 — just over an inch at most — that was worrisome enough.

“We are already in a critical situation, and every increase of even a centimeter causes huge stability problems,” Mr. Stevens said. “You cannot ignore it.”

To give the Minaret of Jam’s tilt some context, the Leaning Tower of Pisa once tilted 5.5 degrees from vertical and, after $25 million in emergency work, including massive counterweights, that tilt was reduced to 3.99 degrees. Even at that, the top of the Tower of Pisa leans nearly 13 feet from the perpendicular.

Jam is about 3.47 degrees out-of-kilter, but it is 30 feet taller. And while Pisa is made of quarried stone, Jam is made of fired clay bricks and lime mortar — not nearly as sturdy a material. Already, its tilt has made the top of the minaret lean more than 10 feet away from an ideal vertical.

“The structural engineers are not going to be happy about this,” Mr. Stevens said.

In addition to stabilizing the monument, Unesco would like to improve protection of the entire area, where there are numerous other ruins — and many illegal digs, as well, from Afghan tomb raiders. A short distance away, archaeologists have located a Jewish cemetery even more ancient than the Minaret of Jam, with headstones inscribed in Hebrew and Persian.