WASHINGTON—Some top Republican lawmakers are urging Attorney General Jeff Sessions to resist any pressure to quit following criticism from President Trump, and to stay in the job at least through the midterm elections.

The same morning as Mr. Trump was venting his frustration at the Justice Department, five Republican senators met Mr. Sessions this past Thursday for breakfast in his personal dining room on the fifth floor of the department’s headquarters. Their message: Hang in there despite Mr. Trump’s broadsides, according...