Cantor, who represents Virginia’s 7th District, told the Richmond Times-Dispatch that he wants Gov. Terry McAuliffe to call for a Nov. 4 special election to fill his seat, a move he said would ensure his constituents are represented in the lame duck session of Congress that is likely to take place after the election.
Cantor resigned from the GOP leadership on Wednesday. He lost a GOP primary in May to economics professor Dave Brat.
Brat plans to run in the special election.
"Right now, I'm focused on winning on November 4th," Brat said in a statement."If I'm fortunate enough to be chosen by the people of the Seventh District to be their next Congressman, I'll come to the office on November 5th ready to serve."
Cantor told the Times-Dispatch that he has not decided what he plans to do now that his congressional career has come to an end.
Cantor served nearly 14 terms, much of it in the GOP leadership.
Cantor took office in 2001 and became majority leader in 2011.