Maryland’s bid for a new FBI headquarters got a boost Friday when the federal General Services Administration changed its criteria for selecting a site, giving less weight to a location near facilities in Quantico, Va., and more weight to cost and social impact.

Virginia had seemed to have the advantage in the sweepstakes for the multimillion-dollar headquarters, which carries some 7,500 jobs, but Maryland’s congressional delegation and Gov. Wes Moore, a Democrat, put up a spirited argument that the federal government was failing to prioritize values other than simple convenience.

“We are encouraged to see today’s announcement from the General Services Administration corrects the flawed approach released in September that ignored taxpayer costs and the Biden-Harris Administration’s commitment to equity. Today’s revised guidelines are a critical step in the right direction,” Moore and the state’s congressional delegation said in a joint statement.

A spokesperson for Virginia Gov. Glenn Youngkin, a Republican, did not immediately respond to a request for comment.

In a joint statement, Virginia Democratic Sens. Tim Kaine and Mark R. Warner expressed dismay about the changes.

“The GSA didn’t pluck its initial criteria out of thin air — it spent years talking to experts and carefully deliberating on what is best for the mission of the FBI,” the senators wrote. “While we are concerned that these changes to the criteria will further delay what has already been a drawn-out, decade-long process to select a new site to replace the dilapidated headquarters downtown, we remain confident that Virginia continues to be a home run in every category, and encourage the GSA to draw this process to a close sooner rather than later.”

The news came as Republicans in Congress escalated an effort to derail the project entirely. Angry about the bureau’s involvement in investigations of former President Donald Trump, some conservatives are threatening to either block funding for a new headquarters or move it far from the Washington region altogether.

On Friday, House Speaker Kevin McCarthy, R-Calif., told reporters that he opposes building a centralized FBI headquarters in the D.C. area.

“This idea that we’re going to build a new big Pentagon and put all the FBI mainly in one place I don’t think is a good structure,” McCarthy said at a news conference in the Capitol, adding that he favors scattering FBI facilities across many locations.

“They’re asking for billions (for the new facility) and I just don’t think that’s the best use or the best structure,” McCarthy said.

Earlier this week, Rep. Jim Jordan, R-Ohio, proposed moving the FBI headquarters to Huntsville, Ala., and other Republicans have suggested withholding salaries for agency officials.

Kaine was traveling Friday but dismissed Jordan’s proposal Wednesday to move the headquarters as a stunt.

“I don’t think it’s a serious proposal, Kaine said. “It demonstrates that Jim Jordan and anybody who would support an amendment like that … have profound disrespect for federal law enforcement agencies.”

Rep. Jen A. Kiggans. R-Va., had stood with McCarthy for most of his news conference, but her office did not immediately respond when asked later whether she agrees that the headquarters should not be in Virginia.

The FBI has long sought a replacement for its offices in the decrepit J. Edgar Hoover building in downtown D.C. Though the agency itself had shown preference for staying in the District to be near the Justice Department, Congress and the union representing FBI agents pushed for a suburban location for the roughly 7,500 employees who work at the headquarters.

The search has settled on sites in suburban Maryland and Virginia, touching off an intense competition between the states. Delegations from each made their cases to the General Services Administration earlier this year. In June, a letter from the FBI boosted Virginia’s case, saying that the agency would benefit from being close to its training facility in Quantico.

At that time, the GSA was operating under a site formula that gave top priority to being near other facilities related to the FBI’s mission, such as its Quantico training complex. The next priority was ease of transportation. Both of those criteria were seen as advantages for Virginia.

However, Moore, the nation’s only elected Black governor, pledged to get the FBI to relocate to majority-Black Prince George’s County, calling on President Joe Biden to deliver on promises to work for equity and to invest in historically underfunded communities.

Moore also questioned why the FBI would locate in Virginia when its Republican leaders — particularly Youngkin and state Attorney General Jason S. Miyares — have criticized the agency for its targeting of Trump over allegations of improper handling of classified documents.

Pushing for Maryland’s interests, Rep. Steny H. Hoyer, D-Md., got language inserted into this year’s federal spending bill requiring the GSA to reconsider its siting criteria, particularly related to “mission requirements, sustainable siting and equity.”

On Friday, GSA officials announced that the agency had lowered the importance of being near other FBI facilities to 25% from 35%, and the importance of transportation to 20% from 25%. It then boosted cost and social equity to 20% each.

“The consultations with the delegations (from each state) provided valuable feedback, and helped us refine our plan to maximize value for the FBI and the public,” GSA Commissioner of the Public Buildings Service Nina Albert said Friday in a news release. “While the core elements of the site selection plan remain the same … we believe these adjustments will support a process that results in a site that best serves the FBI and the public for years to come.”

The agency continues to focus on three sites it identified in 2014: Greenbelt and Landover in Maryland and Springfield in Virginia.

Some congressional Republicans vowed this week to work against that process after hauling FBI director Christopher A. Wray before the House Judiciary Committee to accuse him of a vendetta against conservatives. Wray, who was appointed by Trump, called that charge “somewhat insane,” given his background as a Republican.

McCarthy had not weighed in on the issue until Friday, when he was asked about it by reporters in the Capitol.

“I don’t know that moving to Huntsville is the answer,” McCarthy said, referring to Jordan’s Alabama proposal. “I personally think structure dictates behavior. I’d like to see the structure of a much smaller FBI administration building and more FBI agents out across the country, helping us keep the country safer.”

McCarthy’s opposition could jeopardize funding in the House, setting up a conflict with the Democratic-controlled Senate over moving forward with any new FBI headquarters.