WASHINGTON—Even as President Donald Trump signed a bill Wednesday imposing tough sanctions on Russia for interfering in the 2016 election, he called the law “seriously flawed” and said parts limiting his power to lift the penalties were unconstitutional.

The measure marks some of the strongest action Congress has taken against Russia since the Cold War, and Mr. Trump said he signed it “for the sake of national unity.” But in a pair of statements released after the signing, he said the bill, which requires the president to...