White House counselor Kellyanne Conway said Thursday that President Trump will "stick to building that wall" even as congressional leaders push back on his threat of a government shutdown to secure funding for the structure.

"He's going to stick to building that wall," Conway told Fox News on Thursday. "And he wants the money to pay for it. The president ran on building the wall, won on building the wall, and has remained steadfastly committed to doing it. Anybody who's surprised by that has not been paying attention for over two years."

During a campaign-style rally in Phoenix on Tuesday, the president threatened to shut down the government if he didn't receive funding to build a wall along the U.S. border with Mexico. Trump ran on the promise to build the wall during the campaign, but also promised Mexico would pay for the wall and it wouldn't cost taxpayers any money. He's since backed off that promise.

But Republican and Democratic leaders have rejected the president's threat of a shutdown, saying it's unnecessary.

Conway also addressed Trump's ongoing feud with Sen. Jeff Flake, R-Ariz., who the president has accused several times of being "weak" on borders and crime.

Trump has also signaled his support for Kelli Ward, who is challenging Flake, in the Arizona Republican primary.

"We certainly hope that Sen. Flake will continue to support the agenda that he ran on and that the president ran on," Conway said. "That includes repealing and replacing Obamacare. ... We also know that Sen. Flake is for lower taxes. We hope we can rely on him for tax reform. On the border issue, this is something that the president has been very, very strong and very solid on, and we do hope that members of Congress in the House and the Senate continue to support that."

Flake has been an outspoken critic of the president since before the election, when he refused to support Trump after a video from an appearance of "Access Hollywood" surfaced before the election, on which the president made vulgar comments about women.

The Arizona Republican hasn't backed down from opposing Trump as he promotes his new book, The Conscience of a Conservative, which is a scathing critique of the 2016 election and the president.

Conway reiterated the White House wants the backing of Republicans in Congress, but took a subtle jab at some who she accused of wanting to go on TV rather than helping "behind the scenes."

Flake appeared on Fox News an hour after Conway.

"We really do want the support of the Senate and the members of Congress," she said. "Many of them like to go on TV rather than help behind the scenes. I'll leave that to them to decide where their best and highest use is, but we prefer to have help behind the scenes too on policy issues that these senators have ran successfully on for years, if not decades."