Trump vs McCain: Game on. (AP Photo/Charlie Neibergall, File)

This story has been updated.

If you challenge Donald Trump, he may encourage others to challenge you.

In recent days, the combative Republican presidential candidate has urged Arizona treasurer Jeff DeWit to take on Sen. John McCain, a Trump critic, in the state’s 2016 GOP Senate primary.

Trump and DeWit met privately in Phoenix July 11 aboard Trump’s Boeing 757. During the conversation, which was observed by The Washington Post, Trump and DeWit discussed McCain and what it would take it make the race competitive.

“You really should think about doing it,” Trump told DeWit, who nodded as he sat inches from Trump in the cream-colored cabin.

[Donald Trump now thinks John McCain, who he called ‘very bright’ in 2008, is a ‘dummy’]

As Trump detailed what he sees as McCain’s vulnerabilities — ties to the GOP establishment, longtime support for immigration reform -- DeWit agreed that the upcoming primary could become a marquee contest for conservatives.

Businessman and TV personality Donald Trump is a possible Republican contender for the White House in 2016. Here's his take on Obamacare, building a border wall, and more, in his own words. (Julie Percha/The Washington Post)

But DeWit told Trump that his friend, state Sen. Kelli Ward, is already running against McCain, making his own entry unlikely unless circumstances changed. Trump said he understood DeWit’s position but told him it’d be smart to leave his options open and think seriously about a bid.

Reached Friday by phone, DeWit said the meeting with Trump was about getting to know the real-estate mogul. “With 100 percent certainty I won’t be running for U.S. Senate in 2016. I appreciate Mr. Trump’s suggestion but really enjoy being Arizona's state treasurer.”

In an e-mail Friday, Trump campaign manager Corey Lewandowski said Trump “has not spoken to any other” Arizona Republicans about possibly running against the 78-year-old senator.

Ward, 46, formally announced her campaign Tuesday. Other possible primary contenders, such as Reps. David Schweikert and Matt Salmon, have so far expressed little interest in taking on the incumbent and former Republican presidential nominee.

Ward has drawn positive coverage from conservative news organizations such as Breitbart and talk-radio programs. “I am jumping into this knowing full well that this is a David and Goliath battle, but remember, David won that one,” Ward said Tuesday during her campaign’s launch.

Not everyone on the right, however, is enthusiastic about Ward’s candidacy. FreedomWorks, a powerful conservative organization, has already expressed skepticism about her record and her viability, and the Senate Conservatives Fund, another group, has declined to endorse her.

According to the Arizona Republic, Ward has drawn scrutiny for once exploring “the idea that airplanes are spraying dangerous ‘chemtrails’ into the air — a conspiracy theory she subsequently has said she never believed — and for traveling to Nevada in 2014 to show support for controversial rancher Cliven Bundy, who was in a standoff with the U.S. Bureau of Land Management over grazing fees and cattle.”

On the Democratic side, Rep. Ann Kirkpatrick, a two-term House member from eastern Arizona, announced her Senate campaign in May.

Appearing Friday on MSNBC’s “Morning Joe,” Trump said he supported McCain’s 20o8 presidential campaign but made clear that their relationship has disintegrated as McCain has voiced concern about Trump’s rhetoric on illegal immigration.

“I think he will lose in the primary,” Trump said. “If the right person runs against him, they’ll win in the primary. He’s not very popular there anyway.”

“He was very nasty to me,” Trump added. “My attitude is this: if a person is nice to me, I will go out of my way to be nice to that person.”

[Donald Trump is now essentially guaranteed a spot on the debate stage]

McCain, in an interview with The New Yorker published this week, said Trump’s rally in Phoenix last Saturday was “very hurtful to me. Because what he did was he fired up the crazies.”

Trump wrote Thursday on Twitter that McCain “should be defeated in the primaries. Graduated last in his class at Annapolis--dummy!”

Brian Rogers, a McCain adviser, declined to comment on Trump’s efforts to topple the senator.