Senate Majority Leader Mitch McConnell (R-Ky.) and President Trump's relationship is fraying amid Trump's repeated public attacks and controversial statements. (Jenny Starrs/The Washington Post)

Amid reports of a widening rift between President Trump and Senate Majority Leader Mitch McConnell, both Republican leaders issued statements Wednesday talking up their “unity” on key GOP agenda items.

Trump has waged a public war with McConnell (R-Ky.) in recent weeks, blaming him for the Senate's failure to approve the Republicans' health-care bill and pushing him to change Senate rules so that most legislation would require only a simple majority to be approved. Trump has also attacked Sen. Jeff Flake (R-Ariz.) against the wishes of McConnell, who hopes to see Flake reelected.

On Tuesday, the New York Times reported that McConnell was seething at Trump's public criticism and that the two had not spoken since a heated phone call this month about health care and the ongoing Russia investigation that has dogged the Trump administration.

In a statement Wednesday afternoon, White House press secretary Sarah Huckabee Sanders said that Trump and McConnell “remain united on many shared priorities, including middle class tax relief, strengthening the military, constructing a southern border wall and other important issues.”

She seemed to acknowledge that the two do not plan to speak until Congress returns from the August recess after Labor Day.

“They will hold previously scheduled meetings following the August recess to discuss these critical items with members of the congressional leadership and the president’s Cabinet,” Huckabee Sanders said. “White House and leadership staff are coordinating regarding the details of those meetings.”

A rift between Trump and McConnell would be a highly unusual roadblock for a president in his first term hoping to move forward with major legislation in a Congress controlled by his party.

Come September, Congress must approve funding for the government for the remainder of the year and increase the debt limit to keep the government open. The White House hopes to also revisit health-care legislation and tackle a tax overhaul.

In his own statement, McConnell more sharply refuted the reports of conflict with Trump.

“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,” McConnell said.

In ticking off the list of priorities, McConnell included providing “relief from Obamacare,” a turn of phrase that seemed to stop short of the Republican Party's mantra of “repeal and replace.” And unlike the White House, McConnell made no mention of funding for the border wall.

At a rally in Phoenix on Tuesday night, Trump seemed to imply that he would hold up funding for the government if the wall funding was not approved, a pledge that contradicts congressional Republican leadership. He had promised during his campaign that Mexico would pay for the wall.

McConnell has been more vague about whether he supports the wall and has unequivocally dismissed the idea that Mexico would ever pay for it.