WASHINGTON—Since taking office, President Trump has criticized Ukraine for corruption and expressed sympathy with Russia’s historical claim to parts of the country—views that have tempered his engagement with Ukraine.

Mr. Trump’s skepticism on Ukraine was fueled even before he took office when, in the thick of the 2016 election, the country’s anticorruption agency released information alleging payments to Trump campaign manager Paul Manafort. Mr. Trump’s views on Ukraine are now an important backdrop to the impeachment hearings...