House Speaker John A. Boehner (R-Ohio)  in September 2013. (J. Scott Applewhite/AP)

Updated 3:22 p.m.

House Speaker John A. Boehner (R-Ohio) said Monday that he intends to run again to lead his Republican colleagues in the House — but left open the possibility that he might not complete his next term.

During a wide-ranging conversation about politics and policy hosted by the San Antonio Chamber of Commerce, Boehner said that he is running for reelection and "I expect to be speaker" after November's elections.

"This issue comes up from time to time. I have a very good relationship with my colleagues on both sides of the aisle. Even in my party, even with some people with which we have disagreement almost every day, I have a good relationship with them as well. It’s open, it’s honest and it’s straightforward. So, I'm looking forward to it."

But Boehner stopped short of committing to serve a full term if he wins reelection in November.

"Listen, I can't predict what’s going to happen. I'm going to be 65 years old in November. I never thought I'd live to be 60 so I’m living on borrowed time," Boehner said in response to a question from Texas Tribune CEO and Editor-in-Chief Evan Smith.

Boehner's comments came during a remarkably candid conversation with Smith, who asked a series of question on a variety of subjects.

Regarding allegations of corruption and avoidable deaths at a Department of Veterans Affairs hospital in Phoenix, Boehner once again voiced support for Veterans Affairs Secretary Eric Shinseki.

"I want to keep the focus on fixing the problem, not fixing the personalities," Boehner said.

On immigration, Boehner reiterated that he'd like to see a "bite-sized" legislative approach in the House that would begin by tackling concerns with border security. But he acknowledged that some of his GOP colleagues are reluctant to tackle the issue.

"There are some members of my party that just do not want to deal with this," Boehner said. "It’s no secret. But I do believe the vast majority of members of our party do want to deal with this, and they want to deal with this honestly, openly and fairly."

As for presidential politics, Boehner said he would refrain from actively supporting any Republican seeking the 2016 GOP presidential nomination. But he signaled support for two would-be candidates.

"Jeb Bush has been my friend, I think he'd make a great president and I’ve been nudging him for some time," Boehner admitted. Asked about a potential presidential candidacy by Ohio Republican Gov. John Kasich, Boehner offered that "I love John Kasich. We play golf together."

"I'm not endorsing anybody," he said of potential presidential candidates. "We'll let them sort it all out."