Ross D. Franklin/AP Photo

On Monday, New Jersey Gov. Chris Christie addressed reports that suggested he was ready to back a potential challenger to New York Gov. Andrew Cuomo.

In a news conference to announce personnel changes, Christie said he was "stunned" to read reports that said he was ready to support Westchester County executive Rob Astorino for governor if he ran against Cuomo, and said the stories did not describe the meeting correctly.

"He has not said he's running for governor," Christie said of Astorino. "He didn't indicate to me that night that he was running for governor. The nature of our meeting … that was obviously leaked from people in his camp, our meeting was essentially me and [Christie's wife] Mary Pat, with Rob and his wife, asking us about what it was like to run for governor with young children, and to serve as governor with young children."

At the news conference in Trenton, Christie said "that was the entirety of the conversation," and he stressed that Astorino "did not say he was going to run" and he "didn't seek support," adding the foursome didn't even "talk about politics … except as how it related to the family."

Christie became the new head of the Republican Governors Association in Arizona last month at its annual conference. The New York Post reported Christie and Astorino met at the Scottsdale event to discuss whether Astorino should challenge Cuomo. Cuomo was asked about the report last week and told reporters, "I can tell you this: I spoke to Gov. Christie this morning who told me the exact opposite. And I'll leave it at that," according to the New York Observer.

"When Gov. Cuomo called me, to discuss other matters, and brought that issue up, I told him exactly what he related, which was, Rob Astorino never asked me for support, didn't say he was running for governor, nor did I pledge any support," Christie said.

The governor, known for his direct style, also said as head of the RGA he could only support a Republican nominee, not a primary candidate.

"As RGA chairman, we're looking to elect Republican governors in every state. And, once that's cleared up in New York, as to who the Republican candidate might be, then we'll make an assessment at the RGA about the worthiness of investing in that race," Christie said.

"But we've been pretty clear about not getting involved in primaries. There is no indication yet whether there will be one, two, three, four or more candidates in the Republican contest for the gubernatorial nomination. So my statement that I'm not supporting Mr. Astorino has two levels of importance. One, as RGA chairman, I don't support anyone until they're the Republican nominee. And two, because Mr. Astorino hasn't told me or anybody else he's running for governor. "

Christie called the people in Astorino's "camp" who had urged him to wage a fight against Cuomo "irresponsible" for trying to "create an image that I'm urging him to run. I'm not urging him to do anything. He came and asked for time, specifically asked for time, with me and Mary Pat. For he and his wife to meet with the two of us, to talk about the impact this has on your family."

Christie said when there is a Republican nominee for governor of New York he would "support the Republican nominee," but he did say that putting money into the race is a decision that needs to be made down the road, and it is not a definite one.

"The fact is whether the RGA will invest in that race is a question based upon the competitiveness of the other governor races and the competitiveness of that race. As [former RGA chairman and Mississippi governor] Haley Barbour told me, a long time ago when he had the job, the RGA does not invest in lost causes and it doesn't pay for landslides. We go into places where we can make a difference. And that's what we will do, in New York, and make that assessment at the time."

At the news conference, which was called to announce Christie would be nominating his chief of staff to attorney general, as well as replacing him with a new chief of staff, Christie was also asked about whether he is now the front-runner for the 2016 Republican presidential nomination, but called any claims like that "meaningless."

"It's December of 2013," Christie said. "It is completely meaningless. It has no effect on me nor do I give it any much thought. It just doesn't matter. It will change any number of times between now and then."

ABC's Nicole Rossoll contributed to this report.