A nonpartisan government watchdog says it can't currently determine whether building President Trump's southern border wall is the most effective use of federal funds, and that the project is at an "increased risk" of costing "more than projected."

The Government Accountability Office (GAO) has released a report outlining concerns about the cost and effectiveness of one of the president's signature campaign promises. Mr. Trump originally said Mexico would pay for the wall, but has since threatened a government shutdown if he doesn't get the $25 billion he wants to build the wall and boost border security.

So far, the president has received only a small portion of that funding from Congress, which is wary of launching a battle over immigration ahead of the 2018 midterm elections. Contractors have already built wall prototypes for U.S Customs and Border Protection, which is under the umbrella of the Department of Homeland Security, after Mr. Trump issued an executive order immediately after taking office directing the homeland security secretary to plan, design and build physical barriers along the U.S.-Mexico border.

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"DHS plans to spend billions of dollars developing and deploying new barriers along the southwest border," GAO concluded in its report. "However, by proceeding without key information on cost, acquisition baselines, and the contributions of previous barrier and technology deployments, DHS faces an increased risk that the Border Wall System Program will cost more than projected, take longer than planned, or not fully perform as expected."

"Without assessing costs when prioritizing locations for future barriers, CBP does not have complete information to determine whether it is using its limited resources in the most cost-effective manner and does not have important cost information that would help it develop future budget requests. Without documenting plans to require CBP to follow the DHS acquisition process for the San Diego barrier segment, DHS may not establish cost, schedule, and performance goals by which it can measure the program's progress."

GAO recommended that the CBP commissioner analyze the costs associated with future barrier segments along the border and include cost as a factor in its prioritization strategy. The government watchdog also said DHS' undersecretary for management should document its plans to follow DHS' acquisition cycle.

DHS spokeswoman Katie Waldman said walls have proven extremely effective, and Americans deserve a secure border.

"Walls have proven to be extremely effective at deterring illegal entries and the smuggling of illicit drugs into the United States," she said. "The initial prioritization for developing barriers in each location or segment was based on an operational assessment of priorities including current risks and threats, which was followed by a resource analysis that factored in cost. After years of investment in a border wall system, we experienced a roughly 90 percent reduction in apprehensions in the San Diego, El Paso and Yuma Sectors. Americans deserve a secure border that protects our communities and keeps America safe and this administration is doing so by constructing the first border wall in a decade."

Mississippi's Rep. Bennie Thompson, the ranking Democrat on the House Homeland Security Committee, said the GAO report shows what they already believed — that the administration is "fixated on campaign promises no matter the cost or consequences."

"This report exposes what we have suspected would happen for over a year. The Trump Administration, fixated on campaign promises no matter the cost or consequences, is rushing the construction of the President's completely unnecessary border 'wall,'" Thompson said in a statement.

"In moving too fast, they have ignored necessary and established acquisitions protocols and plan to build a multi-billion dollar border wall where their own analysis shows it is not a priority. To be blunt, this administration has no clue what it is doing and must be held accountable. ...Democrats have and continue to support proven border security projects, but we will not sit idly by while billions of American taxpayer dollars to be thrown down the toilet."

The nearly 2,000-mile border already has fencing along 654 of those miles. But so far, Mr. Trump has been unable to secure the funding he needs from Congress, since Mexico has made it clear the country doesn't intend to pay for it. Mr. Trump has expressed a willingness to shut down the U.S. government if needed to get his border wall funding, which concerns some Republicans in reelection battles this year.

"I would be willing to "shut down" government if the Democrats do not give us the votes for Border Security, which includes the Wall!" the president tweeted last week. "Must get rid of Lottery, Catch & Release etc. and finally go to system of Immigration based on MERIT! We need great people coming into our Country!"

I would be willing to “shut down” government if the Democrats do not give us the votes for Border Security, which includes the Wall! Must get rid of Lottery, Catch & Release etc. and finally go to system of Immigration based on MERIT! We need great people coming into our Country! — Donald J. Trump (@realDonaldTrump) July 29, 2018

Pressed on that tweet in a news conference with the Italian prime minister, Mr. Trump repeated that he'd "have no problem doing a shutdown."

— CBS News' Jeff Pegues contributed to this report.