As with the troops in downtown Simferopol, the soldiers did not have markings on their uniforms.

There were also other unconfirmed reports of additional Russian military forces arriving in Crimea, including Russian ships landing in Feodosiya, in eastern Crimea.

Crimea, while part of Ukraine, has enjoyed a large degree of autonomy under an agreement with the federal government in Kiev since shortly after Ukrainian independence from the Soviet Union.

The strategically important peninsula, which has been the subject of military disputes for centuries, has strong historic, linguistic and cultural ties to Russia. The population of roughly two million is predominantly Russian, followed by a large number of Ukrainians and Crimean Tatars, people of Turkic-Muslim origin.

In eastern Ukraine, which is also heavily pro-Russian, demonstrators in Kharkiv rallied and then seized control of a government building, pulling down the blue-and-yellow Ukrainian flag and raising the blue, white and red Russian one. Scores of people were injured as protesters scuffled with supporters of the new government in Kiev.

In Donetsk, also in the east, several thousand people held a rally in the city center, local news agencies reported, with many chanting pro-Russian slogans and demanding a public referendum on secession from Ukraine.

In Moscow, the parliamentary debate on authorizing military action was perfunctory, but laced with remarks that echoed the worst days of the Cold War. Underscoring the extent to which the crisis has become part of Russia’s broader grievances against the West, lawmakers focused on Mr. Obama and the United States as much as on the fate of Russians in Ukraine.

“All this is being done under the guise of democracy, as the West says,” Nikolai I. Ryzhkov, one member of Parliament, said during the debate. “They tore apart Yugoslavia, routed Egypt, Libya, Iraq and so on, and all this under the false guise of peaceful demonstrations.” He added, “So we must be ready in case they will unleash the dogs on us.”

Yuri L. Vorobyov, the body’s deputy chairman, said Mr. Obama’s warning on Friday was a cause for Russia to act. “I believe that these words of the U.S. president are a direct threat,” he said. “He has crossed the red line and insulted the Russian people.”