Mr. Ryzhkov said there was not likely to be another large action until March 11, after presidential elections, when Mr. Putin plans to extend his stretch as Russia’s dominant figure to an eventual 18 years.

City authorities issued permits for crowds of 30,000 and 50,000 in December.

Mr. Medvedev on Monday presented lawmakers with a draft measure that would restore the direct election of governors. The change, long demanded by opposition groups, is seen by many as a response to the large demonstrations.

But vague language in the bill gives the Kremlin a possible tool to filter out undesirable candidates. Parties would have the power to nominate candidates for governor, but only “following consultations with the president, who shall set the procedures for such consultations.”

Aleksei V. Makarkin, an analyst with Moscow’s Center for Political Technologies, said the authorities and opposition leaders alike were waiting to see the size of the crowd that gathers on Feb. 4. A crowd of 20,000 or 30,000 would suggest that Mr. Putin is emerging from the danger of a political force capable of challenging his power, he said; if the crowd is larger than on Dec. 24, when it was estimated at 80,000, the authorities might prepare to negotiate. Some polling agencies have shown a rise in Mr. Putin’s approval ratings since late December.

In the article published Monday, Mr. Putin takes a skeptical view of the mobilization that took place in December, expressing irritation at the protesters’ lack of a clear agenda. “Today people are talking about various forms of renewal of the political process,” he wrote. “But what are we supposed to be negotiating about? About how our power should be structured? Whether it should be given to ‘better people’? And after that — what? What will we do?”

Mr. Putin said Russia would have to weather a long, painful period of global turbulence, in which economic shocks have converged with social and ethnic tension and in which other nations — presumably referring to the United States — are fueling uprisings.

“In a number of regions, we hear the declarations of aggressively destructive forces, ultimately threatening the stability of all the peoples of the earth,” Mr. Putin wrote. “Objectively, their allies turn out to be those states that are trying to ‘export democracy’ with the assistance of forceful, military means.”