He was among Mr. Christie’s guests during ceremonies held at ground zero 10 years after the Sept. 11 attacks. Rabbi Carlebach and three other rabbis watched from the 21st floor at the unfinished 1 World Trade Center, and he told the website New Jersey Jewish News that the governor “spent a couple of hours mingling with us.”

In 2012, Rabbi Carlebach was part of a group that traveled with the governor to Israel on an “economic mission” to increase trade between New Jersey and Israel. He was also invited to the governor’s official residence, Drumthwacket, to light Hanukkah candles.

Rabbi Carlebach says he has been a longtime supporter of Mr. Christie, and he was listed as a Middlesex County co-chairman in the Jewish Leaders for Christie coalition, according to an email from the governor’s re-election campaign on Sept. 3.

But in the interview, Rabbi Carlebach, who has also served as a chaplain of the Port Authority Police Department, made a distinction between supporting and endorsing a candidate. “I never came out publicly and endorsed,” he said. “I am a clergyman. As a policy I don’t endorse, but I support the governor.”

In a statement on Thursday night, Rabbi Carlebach called his work “apolitical” and said he had worked with “a number of governors and their administrations.”

Rabbi Carlebach said he did not recall whether Mr. Christie or any of his representatives asked him to consider endorsing the governor more explicitly. He recalled meeting Mr. Boehner in 2008, most likely at a Republican convention where he worked as a chaplain. He attended another convention in 2012 but said he did not remember meeting Mr. Boehner then.

Image Bridget Anne Kelly, former deputy chief of staff for Mr. Christie. Credit... North Jersey Media Group via, Reuters

Though Mr. Boehner has expressed support for Mr. Christie in recent weeks, the two have had an at times fractious relationship. Last year, after a bill to aid victims of Hurricane Sandy did not come to a vote in the House, Mr. Christie assailed Mr. Boehner’s leadership.