Ukrainians, including most Russian speakers, want to keep their country united with its current borders intact, but there are concerns about the government. While few Ukrainians have confidence in President Vladimir V. Putin of Russia, his reputation has grown considerably at home, with more than 80 percent of Russians trusting his handling of world affairs.

These are some of the results of two polls conducted by the Pew Research Center last month, after the annexation of Crimea but before recent violence in several Ukrainian cities.

Ukrainians have also become more distrustful of Russia in general. Two-thirds of Ukrainians say that Russia is a bad influence on their country. In 2009, only a quarter considered its impact as a negative. The evaluation of the United States improved slightly over the same period, while the European Union was seen as about the same. Yet while Russian speakers in Ukraine are divided over the influence of Russia, they are much more negative about both the United States and the European Union.

Although few in the international community acknowledge the validity of Crimea’s secession from Ukraine, Russians overwhelmingly say the government in Kiev should recognize the referendum results and allow Crimea to join Russia.