The survey results were released as the pro-Russia forces were considering whether to go ahead with a referendum on autonomy planned for Sunday in defiance of a call from Russian President Vladimir Putin to delay the vote. A decision was expected later in the day.
The organisers have said the referendum was on whether to give the eastern regions more autonomy within Ukraine, but they have left open the possibility of using it to seek independence or annexation by Russia.
Many fear that such a vote could be a flash point for further violence between Ukrainian troops and the militants who have seized government buildings in about a dozen cities in the east.
The poll conducted last month by the Washington-based Pew Research Centre found that 77% of people nationwide want Ukraine to maintain its current borders, while nearly as many, or 70%, in the east feel the same. Only among Russian speakers does the percentage drop significantly, but it is still over half at 58%.
The central government in Kiev has the confidence of only about 41% of Ukrainians, with a sharp divide between the west of the country, where support is 60%, and the east, where it is a low 24%, according to the poll.
Russia, however, is viewed with great suspicion, with three times as many Ukrainians surveyed saying Russia is having a bad influence on their country as say its impact is positive.
In Crimea, which Russia annexed in March following a referendum, 93% of people surveyed expressed confidence in Putin and said Russia was playing a positive role on the peninsula. Their confidence in US President Barack Obama, on the other hand, was recorded at a dismal 4%.
The poll in Ukraine was conducted April 5-23 among 1,659 adults, and the one in Russia April 4-20 among 1,000 adults. Both have a margin of error of about 3.5 percentage points.
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