Negative feelings about President Vladimir V. Putin have appeared to increase across Russia since Ukrainian troops pushed into Russian territory two weeks ago, according to a firm that tracks attitudes in the country by analyzing social media and other internet postings.

While news outlets in Russia have tried to put a more positive spin on the developments in the war, focusing on the Russian government’s humanitarian response, some Russian social media users have expressed discontent.

Many of the online postings, according to the analysis by FilterLabs AI, say Ukraine’s advance is a failure of the Russian government and, more specifically, Mr. Putin.

It is difficult to accurately gauge public opinion in Russia, or any other authoritarian country, because people responding to polls often give answers that they think the government wants. To address that shortcoming, FilterLabs tracks comments on social media sites, internet postings and news media sites, using a computer model to analyze sentiments expressed by ordinary Russians.

Positive attitudes about Mr. Putin took a hit last year after a short-lived armed rebellion led by Yevgeny Prigozhin, the head of a Russian paramilitary force. But the shift in sentiment has appeared sharper in the days since Ukrainian troops launched their incursion into the Kursk region of western Russia.

“Putin’s response to the incursion was seen as inadequate at best and insulting at worst,” said Jonathan Teubner, the chief executive of FilterLabs.