“Each of you will have the chance to render your verdict on the Democrats’ conduct at the ballot box,” Mr. Trump said.

He targeted Senator Richard Blumenthal, Democrat of Connecticut, as “Da Nang Dick” for falsehoods about his military service during the Vietnam War. And calling her “Leaking Dianne Feinstein,” the president laced into the top Democrat on the Senate Judiciary Committee for her fumbled denial that her staff had leaked a letter laying out the first allegation of sexual misconduct against Judge Kavanaugh.

“No, no, no, no, I didn’t. I don’t think. Wait, did we leak?” Mr. Trump said, mocking Ms. Feinstein, Democrat of California, who had turned toward her aides to confirm her answer during a congressional hearing. “Was that the worst body language you’ve ever seen?”

Mr. Trump did cede the spotlight for a bit to a few Republican candidates, including Kris Kobach, the party’s nominee for governor, who is known for his hard-line immigration views and his unfounded claims on voter fraud.

“I hope he loses because I want him so badly,” Mr. Trump said of Mr. Kobach, who served as vice chairman of the president’s voter fraud commission, which did not find any sign of widespread election fraud.

“But don’t do that,” he added.

The president’s rally — his fourth of the week, with four more to come next week — was in part designed to propel conservative turnout in the midterm elections next month and to maintain what Mr. Trump described as “a momentum that hasn’t been seen in years.”

But the president also extended his vision to his own re-election, listing the Democratic opponents he told the crowd he is eager to defeat: Senators Cory Booker and Elizabeth Warren, and former Vice President Joseph R. Biden Jr.