WASHINGTON — The White House brokered an agreement on Monday with intelligence and law enforcement officials that will allow Republican congressional leaders to view some of the most highly classified information related to the Russia investigation, administration officials said.

For months, a small group of lawmakers close to Mr. Trump have been in a pitched fight with the Justice Department over access to some of its most delicate case files, including documents detailing the scope of the Russia investigation by Robert S. Mueller III, the special counsel.

They have trained their focus most recently on access to documents and information related to a secret informant used by F.B.I. agents to gather information from Trump associates who were overseas during the 2016 presidential campaign. Representative Devin Nunes, Republican of California and the House Intelligence Committee chairman, has threatened to hold Rod J. Rosenstein, the deputy attorney general who is overseeing the Russia inquiry, in contempt of Congress or to try to impeach him if he does not hand over the material.

Until Monday, intelligence and law enforcement officials had strenuously resisted both demands, saying that the information was highly sensitive and that it was not appropriate to turn over the unredacted material to Congress, where they fear it could potentially become public or be used to undermine Mr. Mueller’s inquiry. They raised some of their concerns in a letter and then in a face-to-face meeting two weeks ago with Mr. Nunes.