The Russians “have blown through” many of their precision-guided munitions, said the senior U.S. official, who was not authorized to speak publicly on details of Russia’s shortcomings. “In fact, they continue to hit Mariupol with a lot of dumb bombs.”

So-called dumb, or unguided, airdropped munitions, are pre-9/11 relics for the United States and NATO, as Western militaries have now almost completely converted their arsenals with kits that guide bombs to their targets with lasers or G.P.S. satellite signals.

The official also said that sanctions and export controls established after Russia invaded Ukraine had limited Moscow’s access to the kinds of electronic components it needed to build guided weapons, thus affecting Mr. Putin’s ability to restock his military with modern aerial munitions.