MINNEAPOLIS — A fired-up President Trump lashed out against Democrats at a combative campaign rally on Thursday night, deriding them as “very sick and deranged people” who were only investigating him for abuse of power in order to “erase your vote.”

Facing impeachment in the House, Mr. Trump took his case to his core supporters, arguing that Democrats were trying to overturn the 2016 election because they knew they could not beat him in 2020. He singled out former Vice President Joseph R. Biden Jr. as nothing but a toady for President Barack Obama.

“He was only a good vice president because he knew how to kiss Barack Obama’s ass,” Mr. Trump said, a line that drew huge roars of approval from the crowd.

In his first campaign rally since Speaker Nancy Pelosi declared the formal beginning of an impeachment inquiry last month, Mr. Trump was as raw and rancorous as ever, targeting individual Democrats in highly personal terms that no president has used in public and presenting himself as a victim of a partisan conspiracy.