Vice President Pence speaks in support of Cresent Hardy, Republican candidate for the 4th Congressional District, during a campaign event at the Sands Showroom in the Venetian in Las Vegas on Oct. 27. (Chase Stevens/AP)

Vice President Pence declined to say Tuesday whether he supports Rep. Kevin McCarthy (R-Calif.) becoming the next House speaker, adding the decision should be left to members of the chamber.

Pence was asked about McCarthy, considered the front-runner if Republicans maintain control of the House, during an interview with Politico Playbook.

“I support having a Republican speaker of the House,” Pence offered, eliciting laughter from a live audience.

Pressed, he said he considers McCarthy, the House majority leader, to be “an outstanding leader.” But, Pence added, “there are also others who’ve expressed an interest in that.”

McCarthy faces an open challenge from Rep. Jim Jordan (R-Ohio), a founder of the hard-right House Freedom Caucus, in his bid to succeed Speaker Paul D. Ryan (R-Wis.), who is leaving office.

McCarthy has tried to beef up his right flank by focusing on an issue crucial to President Trump — immigration, and in particular Trump’s proposed U.S.-Mexico border wall.

Earlier this month, McCarthy introduced a bill to fully fund the wall at a cost of $23.4 billion and promised to bring it up for a vote after the election.

Marc Short, Trump’s former legislative affairs director, has said he does not expect Trump to take an overt role in the leadership fight.

Pence told Politico “we’ll just leave the decisions about leadership to the men and women who are elected.”

Pence was more definitive about his own future.

Asked whether he would like to be on the GOP ticked as vice president in 2020, he replied:

“It would be the greatest honor of my life to serve a second term with this president.”

Mike DeBonis contributed to this report.