Trump's public chiding of Flake is just another example of the president's actions that threaten to worsen an already tense relationship with Senate Majority Leader Mitch McConnell and his GOP colleagues. McConnell and his allies have sprung to the defense of senators like Flake when Trump criticized them. The Kentucky Republican is also reportedly irked by Trump's calls for the Senate to change its rules — which the president did again in Phoenix on Tuesday night.

But, by 6:30 a.m. Phoenix time, Trump blew up that assurance, tweeting that he is "not a fan" of Flake.

"I will not mention any names," Trump said. "Very presidential, isn't it? Very presidential."

He nodded to GOP Sen. John McCain , lamenting the "one vote" that sank the party's last-ditch attempt to repeal Obamacare last month. He then mentioned the "other senator," Republican Jeff Flake , without naming him, calling him "weak on borders" and "weak on crime."

The president held his tongue Tuesday night. He took only veiled swipes at the Arizona senators he has frequently criticized, without naming them.

President Donald Trump informed his supporters at his Phoenix campaign rally that he was told not to slam senators from Arizona by name.

President Donald Trump speaks with Senate Majority Leader Mitch McConnell, R-Ky., after delivering his address to a joint session of Congress.

The president's provocation of Republican senators comes even though he will need their cooperation to pass key legislative items in the coming months. Upcoming measures include bills to raise the debt ceiling to avert default, fund the government to avoid a shutdown and overhaul the American tax system.

Tax reform, in particular, is an issue the president pressed for during his campaign, and he sees it as fundamental to boosting economic growth.

A New York Times report Tuesday described the president's deteriorating relationship with the GOP Senate leader in great detail. Trump and McConnell have not spoken in weeks, and the senator privately has been skeptical about whether Trump "will be able to salvage his administration," the Times reported.

McConnell "has fumed over Mr. Trump's regular threats against fellow Republicans and criticism of Senate rules," the newspaper said.

In a statement Wednesday, McConnell said he, Trump and both of their teams "have been and continue to be in regular contact about our shared goals." They are working together on issues like creating jobs, raising the debt ceiling, funding the government, and setting the defense budget, among other issues, the statement added.

"We have a lot of work ahead of us, and we are committed to advancing our shared agenda together and anyone who suggests otherwise is clearly not part of the conversation," the senator said.

Late Wednesday, the White House put out a statement saying that McConnell and Trump "remain united on many shared priorities, including middle class tax relief, strengthening the military, constructing a southern border wall, and other important issues."

Still, Trump's Arizona rally is not likely to make their relationship any better.

First, Trump called for Republicans to scrap the filibuster for legislation, which can be used to require that a measure needs 60 votes to pass. Trump has repeatedly slammed the rule, even though the GOP failed to get even 50 votes needed to repeal Obamacare under the budget reconciliation process.

"We have to," Trump said of removing the filibuster. "And if we don't, the Republicans will never get anything passed. You're wasting your time."

"We have to speak to Mitch, and we have to speak to everybody," the president added.

He reiterated the demand on Wednesday morning in a tweet.

Trump: If Republican Senate doesn't get rid of the Filibuster Rule & go to a simple majority, which the Dems would do, they are just wasting time!

Trump's veiled and direct attacks on McCain and Flake are also not likely to make his party's Senate leader any more friendly.

A super PAC that the Times described as "aligned with" McConnell recently released an ad critical of Kelli Ward, the Republican candidate challenging Flake in the GOP primary next year.

McConnell spokesman David Popp told CNBC that Republican senators have made it clear they don't want to change the rule.

The White House did not respond to a request for comment on this article.

The Trump-McConnell relationship and recent White House chaos have put one Trump Cabinet member in a particularly awkward spot. Transportation Secretary Elaine Chao is married to McConnell.

After Trump's widely criticized news conference last week responding to violence at a white nationalist rally in Charlottesville, Virginia, Chao said, "I stand by my man — both of them."