It also was not immediately clear why the Trump Organization objected to the clause.

Amanda Miller, a spokeswoman for the Trump Organization, did not address that account. She merely said both parties had agreed the agency should look elsewhere. “After much consideration, it was mutually determined that it would be more cost effective and logistically practical for the Secret Service to lease space elsewhere,” she wrote in an email.

Pamela A. Dixon, a spokeswoman for G.S.A., declined to comment.

Catherine Milhoan, a spokeswoman for the Secret Service, said on Thursday that the relocation had no impact on the agency’s security plan and that the agency still hoped to find an acceptable space.

“The United States Secret Service continues to work with G.S.A. to obtain permanent work space in an appropriate location,” she said.

The Washington Post first reported the fallout from the leasing dispute on Thursday.

Though Mr. Trump has not visited the 58-floor tower since his inauguration, the Secret Service continues to have a significant role there. The agency is required by statute to protect a president’s primary residence, regardless of whether any members of the first family are there or not.

The agency’s presence has diminished since Melania Trump, the first lady, moved to Washington this summer. But with a mix of retail, commercial and residential space in the tower and two of the agency’s protectees, Mr. Trump’s two adult sons, regularly at work there, it still requires significant resources.