The moves to curb Mr. Nunes by the Democrats as well as by Mr. Boyd, a Trump administration appointee, came during sharply escalating partisan conflict over the Russia investigation. Republicans and conservative commentators have increasingly argued that the investigation derives from a conspiracy by biased law enforcement officials seeking to sabotage President Trump. Democrats, in turn, have accused Republicans of constructing a false narrative in an attempt to undermine the inquiry on behalf of Mr. Trump.

Adding to the rising turbulence, Republicans are also pointing with alarm to newly revealed texts between two F.B.I. officials who were once part of Mr. Mueller’s team, Peter Strzok and Lisa Page. Mr. Mueller removed Mr. Strzok from his team over the summer after learning that the two had exchanged texts expressing a dislike of Mr. Trump.

The Republican memo, which was written by Mr. Nunes’s staff, is said to claim that the F.B.I. abused its powers under the Foreign Intelligence Surveillance Act, or FISA, to spy on the Trump campaign. Democrats did not know it existed until a committee meeting last week, during which its members voted along party lines to share it with the rest of the House.

Republicans, conservative commentators and social media accounts linked to Russian influence networks immediately began calling for the memo’s public release, portraying it as revealing a major scandal. Committee Republicans are reportedly weighing whether to invoke an obscure House rule to make public classified materials.

People familiar with the memo said it centers on a fall 2016 application for a FISA warrant targeting Carter Page, a onetime member of the Trump presidential campaign who had recently visited Russia. The memo is said to stress that the application used information from a former British intelligence agent, Christopher Steele, without adequately explaining to the judge that his research was financed by Democrats.